Question 12 Marks
Add the following expression:
$\frac{3}{5}\text{x},\frac{2}{2}\text{x},\frac{-4}{5}\text{x}$
Answer$\frac{3}{5}\text{x},\frac{2}{3}\text{x},\Big(\frac{-4}{5}\text{x}\Big)$
$=\frac{3}{5}\text{x}+\frac{2}{3}\text{x}+\frac{-4}{5}\text{x}$
$=\frac{9\text{x}+10\text{x}-12\text{x}}{15}$ (LCM of 5, 3 = 15)
$=\frac{19\text{x}-15\text{x}}{15}$
$=\frac{7}{15}\text{x}$
View full question & answer→Question 22 Marks
Find the following product:
$\Big(\text{x}^4+\frac{1}{\text{x}^4}\Big)\Big(\text{x}+\frac{1}{\text{x}}\Big)$
Answer$\Big(\text{x}^4+\frac{1}{\text{x}^4}\Big)\Big(\text{x}+\frac{1}{\text{x}}\Big)$
$=\text{x}^4\times\Big(\text{x}+\frac{1}{\text{x}}\Big)+\frac{1}{\text{x}^4}\times \Big(\text{x}+\frac{1}{\text{x}}\Big)$
$=\Big(\text{x}^4\times \text{x}+\text{x}^4\times\frac{1}{\text{x}}\Big)+\Big(\frac{1}{\text{x}^4}\times \text{x}+\frac{1}{\text{x}^4}\times \frac{1}{\text{x}}\Big)$
$=\text{x}^5+\text{x}^3+\frac{1}{\text{x}^3}+\frac{1}{\text{x}^5}$
View full question & answer→Question 32 Marks
Find the following product:
$a b\left(a^2-b^2\right)$
Answer$=a b \times a^2-a b \times b^2$
$=a^{(1+2)} b-a b^{(1+2)}$
$-a^3 b-a b^3$
View full question & answer→Question 42 Marks
Simplify the following:
$3 x^2+2(x+2)-3 x(2 x+1)$
Answer$3 x^2+2(x+2)-3 x(2 x+1)$
$=3 x^2+2 \times x+2 \times 2-3 x \times 2 x-3 x$
$=3 x^2+2 x+4-6 x^2-3 x$
$=-3 x^2-x+4$
View full question & answer→Question 52 Marks
Add the following expression:
$5 x-2 x^2-8,8 x^2-7 x-9,3+7 x^2-2 x$
Answer$\left(5 x-2 x^2-8\right)+\left(8 x^2-7 x-9\right)+\left(3+7 x^2+2 x\right)$
$=\left(-2 x^2+5 x-8\right)+\left(8 x^2-7 x-9\right)+\left(7 x^2-2 x+3\right)$
$=13 x^2-4 x-14$
$-2\text{x}^2+5\text{x}-8\\\ \ \ 8\text{x}^2-7\text{x}-9\\\ \ \ 7\text{x}^2-2\text{x}+3\\\underline{\overline{13\text{x}^2-4\text{x}-14}}$
View full question & answer→Question 62 Marks
Subtract:
(x - y + 3z) from (2z - x - 3y)
Answer(x - y + 3z) from (2z - x - 3y)
= (2z - x - 3y) - (x - y + 3z)
= 2z - x - 3y - x + y - 3z
= -x - x - 3y + y + 2z - 3z
= -2x - 2y - z
View full question & answer→Question 72 Marks
Find the following product:
$9 x^2(5 x+7)$
Answer$-9 x^2 \times 5 x+9 x^2 \times 7$
$-9 \times 5 \times x^2 \times x+9 \times 7 \times x^2$
$=45 x^{(2+1)}+63 x^2$
$=45 x^3+63 x^2$
View full question & answer→Question 82 Marks
Find the following product:
$(0.8 x-0.5 y)(1.5 x-3 y)$
Answer$(0.8 x-0.5 y)(1.5 x-3 y)$
$=0.8 x(1.5 x-3 y)-0.5 y(1.5 x-3 y)$
$=(0.8 x \times 1.5 x-0.8 x \times 3 y)-(0.5 y \times 1.5 x-0.5 y \times 3 y)$
$=1.2 x^2-2.4 x y-0.75 y x+1.5 y^2$
$=1.2 x^2-3.15 x y+1.5 y^2$
View full question & answer→Question 92 Marks
Add the following expression:
$\frac{3}{4}\text{x}^2, 5\text{x}^2, -3\text{x}^2, -\frac{1}{4}\text{x}^2$
Answer$\frac{3}{4}\text{x}^2+5\text{x}^2+(-3\text{x}^2)+\Big(-\frac{1}{4}\text{x}^2\Big)$
$=\frac{3}{4}\text{x}^2+5\text{x}^2-3\text{x}^2-\frac{1}{5}\text{x}^2$
$=\frac{3\text{x}^2+20\text{x}^2-12\text{x}^2-\text{x}^2}{4}$ (LCM = 4)
$=\frac{23\text{x}^2-13\text{x}^2}{4}=\frac{10\text{x}^2}{4}$
$=\frac{5}{2}\text{x}^2$
View full question & answer→Question 102 Marks
Find the products:
$\Big(\frac{-13}{5}\text{ab}^2\text{c}\Big)\times \Big(\frac{7}{3}\text{a}^2\text{bc}^2\Big)$
Answer$\Big(\frac{-13}{5}\text{ab}^2\text{c}\Big)\times \Big(\frac{7}{3}\text{a}^2\text{bc}^2\Big)$
$=\frac{13}{5}\times \frac{7}{3}\text{a}\times \text{a}^2\times \text{b}^2\times \text{b}\times \text{c}\times \text{c}^2$
$=\frac{-91}{15}\text{a}^{1+2}\times \text{b}^{2+1}\times \text{c}^{1+2}$
$=\frac{-91}{15}\text{a}^3\text{b}^3\text{c}^3$
View full question & answer→Question 112 Marks
Find the products:
$\Big(\frac{-3}{5}\text{s}^2\text{t}\Big)\times \Big(\frac{15}{7}\text{st}^2\text{u}\Big)\times \Big(\frac{7}{9}\text{su}^2\Big)$
Answer$\Big(\frac{-3}{5}\text{s}^2\text{t}\Big)\times \Big(\frac{15}{7}\text{st}^2\text{u}\Big)\times \Big(\frac{7}{9}\text{su}^2\Big)$
$=\frac{-3}{5}\times \frac{15}{7}\times \frac{7}{9}\text{s}^2\times \text{s}\times \text{s}\times \text{t}\times \text{t}^2\times \text{u}\times \text{u}^2$
$=-1\text{s}^{2+1+1}\times \text{t}^{1+2}\times \text{u}^{1+2}$
$=-\text{s}^4\text{t}^3\text{u}^3$
View full question & answer→Question 122 Marks
Find the following product:
$-17 x^2(3 x-4)$
Answer$=-17 x^2 \times 3 x-\left(-17 x^2 \times 4\right)$
$=-17 \times 3 \times x^2 \times x+17 \times 4 \times x^2$
$=-51 \times x^{(2+1)}+68 x^2$
$=-51 x^3+68 x^2$
View full question & answer→Question 132 Marks
Find the following product:
$(7 x+2 y)(x+4 y)$
Answer$(7 x+2 y)(x+4 y)$
$=7 x(x+4 y)+2 y(x+4 y)$
$=(7 x \times x+7 x \times 4 y)+(2 y \times x+2 y \times 4 y)$
$=7 x^2+28 x y+2 x y+8 y^2$
$=7 x^2+30 x y+8 y^2$
View full question & answer→Question 142 Marks
Find the products:
$\left(-4 x^2\right) \times\left(-6 x y^2\right) \times(-3 y)$
Answer$\left(-4 x^2\right) \times\left(-6 x y^2\right) \times(-3 y)$
$=(-4) \times(-6) \times(-3) x^2 \times x \times y^2 \times y$
$=-72 x^{2+1} \times y^{2+1}$
$=-72 x^3 y^3$
View full question & answer→Question 152 Marks
Find the following product:
$2 x^2\left(3 x-4 x^2\right)$
Answer$=2 x^2 \times 3 x-2 x^2 \times 4 x^2$
$=2 \times 3 \times x^2 \times x-2 \times 4 \times x^2 \times x^2$
$=6 \times x^{(2+1)}-8 \times x^{(2+2)}$
$=6 x^3-8 x^4$
View full question & answer→Question 162 Marks
Find the following product:
$\left(9 x^2-x+15\right)(x 2-3)$
AnswerBy column method:
$9 x^2-x+15$
$\frac{\times\left(x^2-3\right)}{9 x^4-x^3+15 x^2}$
$-27 x^2+3 x-45$
$9 x^4-x^3-12 x^2+3 x-45$
$\therefore\left(9 x^2-x+15\right)\left(x^2-3\right)$
$=9 x^4-x^3-12 x^2+3 x-45$
View full question & answer→Question 172 Marks
Add the following expression:
5x, 7x, -6x
Answer5x + 7x + (-6x)
= 5x + 7x - 6x
= 12x - 6x = 6x
View full question & answer→Question 182 Marks
Add the following expression:
$2 x^2-3 y^2, 5 x^2+6 y^2,-3 x^2-4 y^2$
Answer$\left(2 x^2-3 y^2\right)+\left(5 x^2+6 y^2\right)+\left(-3 x^2-4 y^2\right)=4 x^2-y^2$
$\ \ \ \ 2\text{x}^2-3\text{y}^2\\+5\text{x}^2+6\text{y}^2\\-3\text{x}^2-4\text{y}^2\\ \underline{ \overline{\ \ \ \ 4\text{x}^2-\ \ \text{y}^2}}$
View full question & answer→Question 192 Marks
Add the following expression:
$5 a^2 b,-8 a^2 b, 7 a^2 b$
Answer$5 a^2 b+\left(-8 a^2 b\right)+7 a^2 b$
$=5 a^2 b-8 a^2 b+7 a^2 b$
$=12 a^2 b-8 a^2 b$
$=4 a^2 b$
View full question & answer→Question 202 Marks
Find the following product:
$\left(x^2-x y+y^2\right)(x+y)$
AnswerBy column method:
$x^2-x y+y^2$
$\frac{\times(x+y)}{x^3-x^2 y+x y^2}$
$\frac{x^2 y-x y^2+y^3}{x^3+y^3}$
$\therefore\left(x^2-x y+y^2\right)(x+y)=x^3+y^3$
View full question & answer→Question 212 Marks
Find the following product:
$(x-6)(4 x+9)$
Answer$(x-6)(4 x+9)$
$=x(4 x+9)-6(4 x+9)$
$=(x \times 4 x+x \times 9)-(6 \times 4 x+6 \times 9)$
$=4 x^2+9 x-24 x-54$
$=4 x^2-15 x-54$
View full question & answer→Question 222 Marks
Find the following product:
$(2 x+3 y-5)(x+y)$
Answer$(2 x+3 y-5)(x+y)$
$=2 x(x+y)+3 y \times(x+y)-5(x+y)$
$=(2 x \times x+2 x \times y)+(3 y \times x+3 y \times y)-(5 x x+5 \times y)$
$=2 x^2+2 x y+3 y x+3 y^2-5 x-5 y$
$=2 x^2+5 x y-5 x-5 y+3 y^2$
View full question & answer→Question 232 Marks
Find the following product:
$\left(3 x^2+3 x-9\right)(3 x-9)$
AnswerBy column method: $\ \ \ 3\text{x}^2+5\text{x}-9\\\underline{\ \ \ \ \ \ \ \ \times (3\text{x}-9)\ \ }\\ \ \ 9\text{x}^3\ +15\text{x}^2-27\text{x}\\\underline{\ \ \ \ \ \ \ \ \ -27\text{x}^2-45\text{x}+81\ \ }\\\ \ 9\text{x}^3\ -12\text{x}^2-72\text{x}+81$
$\therefore(3\text{x}^2+5\text{x}-9)(3\text{x}-9)$
$=9\text{x}^3-12\text{x}^2-72\text{x}+81$
View full question & answer→Question 242 Marks
Subtract:
$\left(a^2+b^2-2 a b\right)$ from $\left(a^2+b^2+2 a b\right)$
Answer$\left(a^2+b^2-2 a b\right)$ from $\left(a^2+b^2+2 a b\right)$
$=\left(a^2+b^2+2 a b\right)-\left(a^2+b^2-2 a b\right)$
$=a^2+b^2+2 a b-a^2-b^2+2 a b$
$=a^2-a^2+b^2-b^2+2 a b+2 a b$
$=4 a b$
View full question & answer→Question 252 Marks
Find the following product:
$\left(x^2-a^2\right)(x-a)$
Answer$\left(x^2-a^2\right)(x-a)$
$=x^2(x-a)-a^2(x-a)$
$=\left(x^2 \times x-x^2 \times a\right)-\left(a^2 \times x-a^2 \times a\right)$
$=x^3-a x^2-a^2 x+a^3$
View full question & answer→Question 262 Marks
Find the following product:
$5a(6a - 3b)$
Answer$5 a \times 6 a-5 a \times 3 b$
$=5 \times 6 \times a \times a-(5 \times 3 \times a \times b)$
$-30 a^2-15 a b$
View full question & answer→Question 272 Marks
Find the following product:
$\left(x^2+x y+y^2\right)(x-y)$
AnswerBy column method:
$x^2+x y+y^2$
$\frac{\times(x-y)}{x^3+x^2 y+xy^2}$
$\frac{-x^2 y-xy^2-y^3}{x^3-y^3}$
$\therefore\left(x^2+xy+y^2\right)(x-y)=x^3-y^3$
View full question & answer→Question 282 Marks
Find the following product:
$(5 x+7)(3 x+4)$
Answer$(5 x+7)(3 x+4)$
$=5 x(3 x+4)+7(3 x+4)$
$=(5 x \times 3 x+5 x \times 4)+(7 \times 3 x+7 \times 4)$
$=15 x^2+20 x+21 x+28$
$=15 x^2+41 x+28 a$
View full question & answer→Question 292 Marks
Find the products:
$(-4 a b) \times\left(-3 a^2 b c\right)$
Answer$(-4 a b) \times\left(-3 a^2 b c\right)$
$=(-4) \times(-3) a \times a^2 \times b \times b \times c$
$=12 \times a^{2+1} \times b^{1+1} \times c$
$=12 a^3 b^2 c$
View full question & answer→Question 302 Marks
Find the following product:
$1.5 a\left(10 a^2 b-100 a b^2\right)$
Answer$=1.5 a \times 10 a^2 b-1.5 a \times 100 a b^2$
$=1.5 \times 10 \times a \times a^2 b-1.5 \times 100 \times a \times a \times b^2$
$=15 \times a^{(1+2)} b-150 \times a^{(1+1)} \times b^2$
$=15 a^3 b-150 a^2 b^2$
View full question & answer→Question 312 Marks
Find the following product:
$\frac{3}{5}\text{m}^2\text{n}(\text{m}+5\text{n})$
Answer$=\frac{3}{5}\text{m}^2\text{n}\times \text{m}+\frac{3}{5}\text{m}^2\text{n}\times5\text{n}$
$=\frac{3}{5}\times \text{m}^2\times\text{m}\times \text{n}+\frac{3}{5}\times5\times\text{m}^2\times\text{n}\times \text{n}$
$=\frac{3}{5}\text{m}^{(2+1)}\times\text{n}+3\times \text{m}^2\times \text{n}^{(1+1)}$
$=\frac{3}{5}\text{m}^3\text{n}+3\text{m}^2\text{n}^2$
View full question & answer→Question 322 Marks
Find the products:
$\Big(\frac{-1}{27}\text{a}^2\text{b}^2\Big)\times \Big(\frac{-9}{2}\text{a}^3\text{bc}^2\Big)$
Answer$\Big(\frac{-1}{27}\text{a}^2\text{b}^2\Big)\times \Big(\frac{-9}{2}\text{a}^3\text{bc}^2\Big)$
$=\frac{-1}{27}t\times\Big(\frac{-9}{2}\Big)\text{a}^2\times \text{a}^3\times \text{b}^2\times \text{b}\times \text{c}^2$
$=\frac{1}{3\times 2}\text{a}^{2+3}\times \text{b}^{2+1}\times \text{c}^2$
$=\frac{1}{6}\text{a}^5\text{b}^3\text{c}^2$
View full question & answer→Question 332 Marks
Find the following product:
$\frac{7}{2}\text{x}^2\Big(\frac{4}{7}\text{x}+2\Big)$
Answer$=\frac{7}{2}\text{x}^2\times \frac{4}{7}\times \text{x}+\frac{7}{2}\text{x}^2\times 2$
$=\frac{7}{2}\times \frac{4}{7}\times\text{x}^2\times \text{x}+\frac{7}{2}\times 2\times \text{x}^2$
$=2\times \text{x}^{(2+1)}+7\text{x}^2$
$=2\text{x}^3+7\text{x}^2$
View full question & answer→Question 342 Marks
Find the products:
$\left(2 a^2 b^3\right) \times\left(-3 a^3 b\right)$
Answer$=\left(2 a^2 b^3\right) \times\left(-3 a^3 b\right)$
$=2 \times(-3) a^2 \times a^3 \times b^3 \times b \times b$
$=-6 a^{2+3} \times b^{3+1}$
$=-6 a^5 \times b^4$
View full question & answer→Question 352 Marks
Subtract:
$\left(x^2-y^2\right)$ from $\left(2 x^2-3 y^2+6 x y\right)$
Answer$\left(x^2-y^2\right)$ from $\left(2 x^2-3 y^2+6 x y\right)$
$=\left(2 x^2-3 y^2+6 x y\right)-\left(x^2-y^2\right)$
$=2 x^2-3 y^2+6 x y-x^2+y^2$
$=2 x^2-x^2-3 y^2+y^2+6 x y$
$=x^2-2 y^2+6 x y$
View full question & answer→Question 362 Marks
Simplify the following:
a(b - c) - b(c - a) - c(a - b)
Answera(b - c) - b(c - a) - c(a - b)
= a × b - a × c - b × c + b × a - c × a + c × b
= ab + ab - ac - ac - ab + bc
= 2ab - 2ac
= 2a(b - c)
View full question & answer→Question 372 Marks
Find the following product:
$\Big(\frac{2}{5}\text{x}-\frac{1}{2}\text{y}\Big)(10\text{x}-8\text{y})$
Answer$\Big(\frac{2}{5}\text{x}-\frac{1}{2}\text{y}\Big)(10\text{x}-8\text{y})$
$=\frac{2}{5}\text{x}\times (10\text{x}-8\text{y})-\frac{1}{2}\text{y}\times (10\text{x}-8\text{y})$
$=\Big(\frac{2}{5}\text{x}\times 10\text{x}-\frac{2}{5}\text{x}\times 8\text{y}\Big)-\Big(\frac{1}{2}\text{y}\times 10\text{x}-\frac{1}{2}\text{y}\times 8\text{y}\Big)$
$=4\text{x}^2-\frac{16}{5}\text{xy}-5\text{yx}+4\text{y}^2$
$=4\text{x}^2-\frac{41}{5}\text{xy}+4\text{y}^2$
View full question & answer→Question 382 Marks
Find the following product:
$9 t^2\left(t+7 t^3\right)$
Answer$=9 t^2 \times t+9 t^2 \times 7 t^3$
$=9 \times t^2 \times t+9 \times 7 \times t^2 \times t^3$
$=9 \times t^{(2+1)}+63 \times t^{(2+3)}$
$=9 t^3+63 t^5$
View full question & answer→Question 392 Marks
Find the following product:
(3x + 2y - 4)(x - y)
AnswerBy column method:
$3\text{x}+2\text{y}-4\\\underline{{\ \ \ \ }\times (\text{x}-\text{y})\ \ \ \ }\\3\text{x}^2+2\text{yx}-4\text{x}\\\underline{\ \ \ \ \ \ -3\text{xy}-2\text{y}^2+4\text{y}\ \ \ }\\3\text{x}^2-\ \ \text{xy}-4\text{x}\ \ +4\text{y}-2\text{y}^2$
$\therefore (3\text{x}+2\text{y}-4)(\text{x}-\text{y})$
$=3\text{x}^2-\text{xy}-4\text{x}+4\text{y}-2\text{y}^2$
View full question & answer→Question 402 Marks
Find the following product:
$(4 x-3)(2 x+5)$
Answer$(4 x-3)(2 x+5)$
$=4 x(2 x+5)-3(2 x+5)$
$=(4 x \times 2 x+4 x \times 5)-(3 \times 2 x+3 \times 5)$
$=8 x^2+11 x-15$
View full question & answer→Question 412 Marks
Find the following product:
$-4 x^2 y\left(3 x^2-5 y\right)$
Answer$=-4 x^2 y \times 3 x^2-\left(-4 x^2 y \times 5 y\right)$
$=-4 \times 3 \times x^2 \times x^2 \times y+4 \times 5 \times x^2 \times y \times y$
$=-12 \times x^{(2+2)} \times y+20 \times x^2 \times y^{(1+1)}$
$=-12 x^4 y+20 x^2 y^2$
View full question & answer→Question 422 Marks
Find the following product:
$\left(x^4+y^4\right)\left(x^2-y^2\right)$
Answer$\left(x^4+y^4\right)\left(x^2-y^2\right)$
$=x^4\left(x^2-y^2\right)+y^4\left(x^2-y^2\right)$
$=\left(x^4 \times x^2-x^4 \times y^2\right)+\left(y^4 \times x^2-y^4 \times y^2\right)$
$=x^6-x^4 y^2+x^2 y^4-y^6$
View full question & answer→Question 432 Marks
Find the following product:
$(3 m-4 n)(2 m-3 n)$
Answer$(3 m-4 n)(2 m-3 n)$
$=3 m(2 m-3 n)-4 n(2 m-3 n)$
$=(3 m \times 2 m-3 m \times 3 n)-(4 n \times 2 m-4 n \times 3 n)$
$=6 m^2-9 m n-8 n m+12 n^2$
$=6 m^2-17 m n+12 n^2$
View full question & answer→Question 442 Marks
Find the following product:
$10 a^2(0.1 a-0.5 b)$
Answer$=10 a^2 \times 0.1 a-10 a^2 \times 0.5 b$
$=10 \times 0.1 \times a^2 \times a-10 \times 0.5 \times a^2 \times b$
$=1 \times a^{(2+1)}-5 a^2 b$
$=a^3-5 a^2 b$
View full question & answer→Question 452 Marks
Simplity:
(5x - 9y) - (-7x + y)
Answer(5x - 9y) - (-7x + y)
= 5x - 9y + 7x - y
= 5x + 7x - 9y - y
= 12x - 10y
View full question & answer→Question 462 Marks
Answer-8xy from 7xy
= 7xy - 8xy
= (7 - 8)xy
= -xy
View full question & answer→Question 472 Marks
Subtract:
$x^2$ from $-3 x^2$
Answer$x^2$ from $-3 x^2$
$=-3 x^2-x^2$
$=-4 x^2$
View full question & answer→Question 482 Marks
Find the products:
$\frac{2}{3}\text{x}^2\text{y}\times\frac{3}{5}\text{xy}^2$
Answer$\frac{2}{3}\text{x}^2\text{y}\times \frac{2}{5}\text{xy}^2$
$=\frac{2}{3}\times \frac{3}{5}\text{x}^2\times\text{x}\times\text{y}\times\text{y}^2$
$=\frac{2}{5}\times \text{x}^{2+1}\times\text{y}^{1+2}$
$=\frac{2}{5}\text{x}^3\text{y}^3$
View full question & answer→Question 492 Marks
Find the following product:
$8 a^2(2 a+5 b)$
Answer$=8 a 2 \times 2 a+8 a 2 \times 5 b$
$=8 \times 2 \times a^2 \times a+8 \times 5 \times a^2 \times b$
$=16 a^{(2+1)}+40 a^2 b$
$=16 a^2+40 a^2 b$
View full question & answer→Question 502 Marks
Add the following expression:
x -3y + 4z, y - 2x - 8z, 5x - 2y - 3z
Answer(x - 3y + 4z) + (y - 2x - 8z) + (5x - 2y - 3z) = 4x - 4y -7z
$\ \ \ \ \ \ \text{x}-3\text{y}+4\text{z}\\-2\text{x}+\ \ \text{y}-8\text{z}\\\ \ \ \ 5\text{x}-2\text{y}-3\text{z}\\\underline{\overline{\ \ \ \ 4\text{x}-\ 4\text{y}-7\text{z}\ \ }}$
View full question & answer→Question 512 Marks
Find the following product:
$\left(x^3-y^3\right)\left(x^2+y^2\right)$
Answer$\left(x^3-y^3\right)\left(x^2+y^2\right)$
$=x^3\left(x^2+y^2\right)-y^3\left(x^2+y^2\right)$
$=\left(x^3 \times x^2+x^3 \times y^2\right)-\left(y^3 \times x^2+y^3 \times y^2\right)$
$=x^5+x^3 y^2-x^2 y^3-y^5$
View full question & answer→Question 522 Marks
Simplify the following:
a(b - c) + b(c - a) + c(a - b)
Answera(b - c) + b(c - a) + (a - b)
= a × b - a × c + b × c - b × a + c × a - c × b
= ab - ac + bc - ab + ac - bc
= 0
View full question & answer→Question 532 Marks
Find the following product:
$\left(x^2-y^2\right)(x+2 y)$
Answer$\left(x^2-y^2\right)(x+2 y)$
$=x^2(x+2 y)-y^2(x+2 y)$
$=\left(x^2 \times x+x^2 \times 2 y\right)-\left(y^2 \times x+y^2 \times 2 y\right)$
$=x^3+2 x^2 y-x y^2-2 y^3$
View full question & answer→Question 542 Marks
Find the following product: $\left(x^2-5 x+8\right)\left(x^2+2\right)$
AnswerBy column method:
$\text{x}^2-5\text{x}+8\\ \underline{ \ \ \times(\text{x}^2+2)\ \ \ \ \ \ }\\\text{x}^4-5\text{x}^3+8\text{x}^2\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\text{x}^2-10\text{x}+16}\\\text{x}^4-5\text{x}^3+10\text{x}^2-10\text{x}+16$
$\therefore(\text{x}^2-5\text{x}+8)(\text{x}^2+2)$
$=\text{x}^4-5\text{x}^3+10\text{x}^2-10\text{x}+16$
View full question & answer→Question 552 Marks
Find the following product:
$(5 y-1)(3 y-8)$
Answer$(5 y-1)(3 y-8)$
$=5 y(3 y-8)-1(3 y-8)$
$=(5 y \times 3 y-5 y \times 8)-(3 y-8)$
$=15 y^2-40 y-3 y+8$
$=15 y^2-43 y+8$
View full question & answer→Question 562 Marks
Subtract:
(x - y) from (4y - 5x)
Answer(x - y) from (4y - 5x)
= (4y - 5x) - (x - y)
= 4y - 5x - x + y
= 4y + y - 5x - x
= 5y - 6x
View full question & answer→Question 572 Marks
Find the products:
$\Big(\frac{-18}{5}\text{x}^2\text{z}\Big)\times \Big(\frac{-25}{6}\text{az}^2\text{y}\Big)$
Answer$\Big(\frac{-18}{5}\text{x}^2\text{z}\Big)\times \Big(\frac{-25}{6}\text{az}^2\text{y}\Big)$
$=\frac{-18}{5}\times \frac{-25}{6}\text{x}^2\text{x}\times \text{z}^1\times\text{z}^2\times \text{y}$
$=[-3\times(-5)]\times \text{x}^{2+1}\times \text{z}^{1+2}\times \text{y}$
$=15\text{x}^3\text{yz}^3$
View full question & answer→Question 582 Marks
Find the products: $\left(2 a^2 b\right) \times\left(-5 a b^2 c\right) \times\left(-6 b c^2\right)$
Answer$\left(2 a^2 b\right) \times\left(-5 a b^2 c\right) \times\left(-6 b c^2\right)$
$=2 \times(-5) \times(-6) a^2 \times a \times b \times b^2 \times b \times c \times c^2$
$=60 \times a^{2+1} \times b^{1+2+1} \times c^{1+2}$
$=60 a^3 b^4 c^3$
View full question & answer→Question 592 Marks
Find the following product:
$\Big(\frac{3}{4}\text{a}+\frac{2}{3}\text{b}\Big)(4\text{a}+3\text{b})$
Answer$\Big(\frac{3}{4}\text{a}+\frac{2}{3}\text{b}\Big)(4\text{a}+3\text{b})$
$=\frac{3}{4}\text{a}\times (4\text{a}+3\text{b})+\frac{2}{3}\text{b}\times (4\text{a}+3\text{b})$
$=\Big(\frac{3}{4}\text{a}\times 4\text{a}+\frac{3}{4}\text{a}\times3\text{b}\big)+\Big(\frac{2}{3}\text{b}\times 4\text{a}+\frac{2}{3}\text{b}\times 3\text{b}\Big)$
$=3\text{a}^2+\frac{9}{4}\text{ab}+\frac{8}{3}\text{ba}+2\text{b}^2$
$=3\text{a}^2+\frac{59}{12}\text{ab}+2\text{b}^2$
View full question & answer→Question 602 Marks
Find the following product:
$(9 x+5 y)(4 x+3 y)$
Answer$(9 x+5 y)(4 x+3 y)$
$=9 x(4 x+3 y)+5 y(4 x+3 y)$
$=(9 x \times 4 x+9 x \times 3 y)+(5 y \times 4 x+5 y \times 3 y)$
$=36 x^2+27 x y+20 x y+15 y^2$
$=36 x^2+47 x y+15 y^2$
View full question & answer→Question 612 Marks
Find the following product:
$\left(2 x^2-5 y^2\right)\left(x^2+3 y^2\right)$
Answer$\left(2 x^2-5 y^2\right)\left(x^2+3 y^2\right)$
$= 2 x^2\left(x^2+3 y^2\right)-5 y^2\left(x^2+3 y^2\right)$
$= \left(2 x^2 \times x^2+2 x^2 \times 3 y^2\right)-\left(5 y^2 \times x^2+5 y^2 \times 3 y^2\right)$
$= 2 x^4+6 x^2 y^2-5 y^2 x^2-15 y^4$
$= 2 x^4+x^2 y^2-15 y^4$
View full question & answer→Question 622 Marks
Find the following product:
$4 a(3 a+7 b)$
Answer$-4 a \times 3 a+4 a \times 7 b$
$-4 \times 3 \times a^{(1+1)}+4 \times 7 \times a \times b$
$=12 a^2+28 a b$
View full question & answer→Question 632 Marks
Find the products:
$\Big(\frac{-7}{5}\text{x}^2\text{y}\Big)\times \Big(\frac{3}{2}\text{xy}^2\Big)\times \Big(\frac{-6}{5}\text{x}^3\text{y}^3\Big)$
Answer$\Big(\frac{-7}{5}\text{x}^2\text{y}\Big)\times \Big(\frac{3}{2}\text{xy}^2\Big)\times \Big(\frac{-6}{5}\text{x}^3\text{y}^3\Big)$
$=\frac{-7}{5}\times\frac{3}{2}\times \frac{-6}{5}\text{x}^2\times \text{x}\times \text{x}^3\times\text{y}\times \text{y}^2\times \text{y}^3$
$=\frac{63}{25}\text{x}^{2+1+3}\times \text{y}^{1+2+3}$
$=\frac{63}{25}\text{x}^6\text{y}^6$
View full question & answer→Question 642 Marks
Find the following product:
$\left(3 p^2+q^2\right)\left(2 p^2-3 q^2\right)$
Answer$\left(3 p^2+q^2\right)\left(2 p^2-3 q^2\right)$
$=3 p^2\left(2 p^2-3 q^2\right)+q^2\left(2 p^2-3 q^2\right)$
$=\left(3 p^2 \times 2 p^2-3 p^2 \times 3 q^2\right)+\left(q^2 \times 2 p^2-q^2 \times 3 q^2\right)$
$=6 p^4-9 p^2 q^2+2 q^2 p^2-3 q^4$
$=6 p^4-7 p^2 q^2-3 q^4$
View full question & answer→Question 652 Marks
Find the products:
$\Big(\frac{-3}{14}\text{xy}^4\Big)\times \Big(\frac{7}{6}\text{x}^3\text{y}\Big)$
Answer$\Big(\frac{-3}{14}\text{xy}^4\Big)\times \Big(\frac{7}{6}\text{x}^3\text{y}\Big)$
$=\frac{-3}{14}\times \frac{7}{6}\text{x}\times \text{x}^3\times \text{y}^4\times \text{y}$
$=\frac{-1}{4}\text{x}^{1+3}\times \text{y}^{4+1}$
$=\frac{-1}{4}\text{x}^4\text{y}^5$
View full question & answer→Question 662 Marks
Find the following product:
$\left(x^2-3 x+7\right)(2 x+3)$
AnswerBy column method:
$x^2-3 x+7$
$\times(2 x+3)$
$2 x^3-6 x^2+14 x$
$\frac{3 x^2-9 x+21}{2 x^3-3 x^2+5 x+21}$
$\therefore\left(x^2-3 x+7\right)(2 x+3)$
$=2 x^3-3 x^2+5 x+21$
View full question & answer→Question 672 Marks
Find the products:
$\Big(\frac{-3}{4}\text{ab}^3\Big)\times \Big(\frac{-2}{3}\text{a}^2\text{b}^4\Big)$
Answer$\Big(\frac{-3}{4}\text{ab}^3\Big)\times \Big(\frac{-2}{3}\text{a}^2\text{b}^4\Big)$
$=\frac{-3}{4}\times \frac{-2}{3}\text{a}\times \text{a}^2\times \text{b}^3\times\text{b}^4$
$=\frac{1}{2}\text{a}^{1+2}\times\text{b}^{3+4}$
$=\frac{1}{2}\text{a}^3\text{b}^7$
View full question & answer→Question 682 Marks
Find the following product:
$\Big(\frac{1}{5}\text{x}+2\text{y}\Big)\Big(\frac{2}{3}\text{x}-\text{y}\Big)$
Answer$\Big(\frac{1}{5}\text{x}+2\text{y}\Big)\Big(\frac{2}{3}\text{x}-\text{y}\Big)$
$=\frac{1}{5}\text{x}\times \Big(\frac{2}{3}\text{x}-\text{y}\Big)+2\text{y}\times \Big(\frac{2}{3}\text{x}-\text{y}\Big)$
$=\Big(\frac{1}{5}\text{x}\times\frac{2}{3}\text{x}-\frac{1}{5}\text{x}\times \text{y}\Big)+\Big(2\text{y}\times \frac{2}{3}\text{x}-2\text{y}\times\text{y} \Big)$
$=\frac{2}{15}\text{x}^2-\frac{1}{5}\text{xy}+\frac{4}{3}\text{yx}-2\text{y}^2$
$=\frac{2}{15}\text{x}^2+\frac{17}{15}\text{xy}-2\text{y}^2$
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