Question 12 Marks
Using the formula for squaring a binomial, evaluate the following:
$(197)^2$
Answer$(197)^2$
$= (200-3)^2$
$= (200)^2-2 \times 200 \times 3+(3)^2$
$= 40000-1200+9$
$= 40009-1200$
$= 38809$
View full question & answer→Question 22 Marks
Find the following products:
$(7 x+2 y) \times(x+4 y)$
Answer$(7 x+2 y) \times(x+4 y)$
$=7 x(x+4 y)+2 y(x+4 y)$
$=7 x^2+28 x y+2 x y+8 y^2$
$=7 x 2+30 x y+8 y^2$
View full question & answer→Question 32 Marks
Find following products:
$(x+6)(x+6)$
Answer$(x+6)(x+6)$
$= (x+6)^2$
$= x^2+2 \times x \times 6++(6)^2$
$= x^2+12 x+36$
View full question & answer→Question 42 Marks
Expand:
$\left(x^2 y-y z^2\right)^2$
Answer$\left(x^2 y-y z^2\right)^2$
$\left(x^2 y\right)^2-2 x x^2 y \times y z^2+\left(y z^2\right)^2$
$=x^4 y^2-2 x^2 y^2 z^2+y^2 z^4$
View full question & answer→Question 52 Marks
Using the formula for squaring a binomial, evaluate the following:
$(78)^2$
Answer$(78)^2$
$= (80-2)^2$
$= (80)^2-2 \times 80 \times 2+(2)^2$
$= 6400-320+4$
$= 6404-320$
$= 6084$
View full question & answer→Question 62 Marks
Find the following products:
$\left(x^2+x y+y^2\right) \times(x-y)$
Answer$\left(x^2+x y+y^2\right) \times(x-y)$
$=x\left(x^2+x y+y^2\right)-y\left(x^2+x y+y^2\right)$
$=x^3+x^2 y+x y^2-x^2 y-x y^2-y^3$
$=x^3-y^3$
View full question & answer→Question 72 Marks
Expand: $\Big(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}}\Big)^2$
Answer$\Big(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}}\Big)^2$
$=\Big(\frac{\text{x}}{\text{y}}\Big)^2-2\times\text{xy}\times\text{yx}+\Big(\frac{\text{y}}{\text{x}}\Big)^2$
$=\frac{\text{x}^2}{\text{y}^2}-2+\frac{\text{y}^2}{\text{x}^2}$
View full question & answer→Question 82 Marks
Using the formula for squaring a binomial, evaluate the following:
$(999)^2$
Answer$(999)^2$
$= (1000-1)^2$
$= (1000)^2-2 \times 1000 \times 1+(1)^2$
$= 1000000-2000+1$
$= 1000001-2000$
$= 998001$
View full question & answer→Question 92 Marks
Find the value of:
$(8.63)^2-(1.37)^2$
Answer$(8.63)^2-(1.37)^2$
$=(8.63+1.37)(8.63-1.37)$
$=10.00 \times 7.26$
$=72.6$
View full question & answer→Question 102 Marks
Add:
6ax - 2by + 3cz, 6by - 11ax - cz and 10cz - 2ax - 3by
Question 112 Marks
Find following products:
$(2 x-3 y)(2 x-3 y)$
Answer$(2 x-3 y)(2 x-3 y)$
$=(2 x-3 y)^2$
$=(2 x)^2-2 \times 2 x \times 3 y+(3 y)^2$
$=4 x^2-12 x y+9 y^2$
View full question & answer→Question 122 Marks
Find the continues products:
$(x+1)(x-1)\left(x^2+1\right)$
Answer$(x+1)(x-1)\left(x^2+1\right)$
$=\left\{(x)^2-(1)^2\right\}\left\{x^2+1\right\}$
$=\left(x^2-1\right)\left(x^2+1\right)$
$=\left(x^2\right)^2-(1)^2$
$=\left(x^4\right)-1$
View full question & answer→Question 132 Marks
Expand:
$\Big(\frac{3\text{x}}{4}+\frac{2\text{y}}{9}\Big)^2$
Answer$\Big(\frac{3\text{x}}{4}+\frac{2\text{y}}{9}\Big)^2$
$=\Big(\frac{3\text{x}}{4}\Big)^2+2×\frac{3\text{x}}{4}×\frac{2\text{y}}{9}+\Big(\frac{2\text{y}}{9}\Big)^2$
$=\frac{9\text{x}^2}{16}+\frac{1}{3}\text{xy}+\frac{4}{81}\text{y}^2 $
View full question & answer→Question 142 Marks
Find the following products:
$\left(x^2-x y+y^2\right) \times(x+y)$
Answer$\left(x^2-x y+y^2\right) \times(x+y)$
$=x\left(x^2-x y+y^2\right)+y\left(x^2-x y+y^2\right) \\
=x^3-x^2 y+y^2 x+x^2 y-x y^2+y^3 \\
=x^3+y^3$
View full question & answer→Question 152 Marks
Find the value of:
$(82)^2-(18)^2$
Answer$(82)^2-(18)^2$
$=(82-18)(82+18)$
$=(64)(100)$
$=6400$
View full question & answer→Question 162 Marks
Find following products:$\Big(\frac{1}{\text{x}}+\frac{1}{\text{y}}\Big)\Big(\frac{1}{\text{x}}-\frac{1}{\text{y}}\Big)$
Answer$\Big(\frac{1}{\text{x}}+\frac{1}{\text{y}}\Big)\Big(\frac{1}{\text{x}}-\frac{1}{\text{y}}\Big)$$=\Big(\frac{1}{\text{x}}\Big)^2-\Big(\frac{1}{\text{y}}\Big)^2$
$=\frac{1}{\text{x}^2}-\frac{1}{\text{y}^2} $
View full question & answer→Question 172 Marks
Find the following products:
$\left(x^2-3 x+7\right) \times(2 x+3)$
Answer$\left(x^2-3 x+7\right) \times(2 x+3)$
$=2 x\left(x^2-3 x+7\right)+3\left(x^2-3 x+7\right)$
$=2 x^3-6 x^2+14 x+3 x^2-9 x+21$
$=2 x^3-3 x^2+5 x+21$
View full question & answer→Question 182 Marks
Find the following product:
(3x + 2y - 4) × (x - y + 2)
Question 192 Marks
Using the formula for squaring a binomial, evaluate the following:
$(704)^2$
Answer$(704) ${ }^2$
$=(700+4)^2$
$=(700)^2+2 \times 700 \times 4+(4)^2$
$=490000+5600+16$
$=495616$
View full question & answer→Question 202 Marks
Write the quotient and remainder when we divide:
$\left(x^2-4\right)$ by $(x+2)$
View full question & answer→Question 212 Marks
Expand:
$(5 x+11)^2$
Answer$(5 x+11)^2$
$=(5 x)^2+2 \times 5 x \times 11+(11)^2$
$=25 x^2+110 x+121$
View full question & answer→Question 222 Marks
Find following products:
$\Big(\frac{5}{6}\text{a}^2+2\Big)\Big(\frac{5}{6}\text{a}^2+2\Big)$
Answer$\Big(\frac{5}{6}\text{a}^2+2\Big)\Big(\frac{5}{6}\text{a}^2+2\Big)$
$=\Big(\frac{5}{6}\text{a}^2+2\Big)^2$
$=\Big(\frac{5}{6}\text{a}^2\Big)^2+2\Big(\frac{5}{6}\text{a}^2\Big)\times2+(2)^2$
$=\frac{25}{36}\text{a}^4+\frac{10}{3}\text{a}^2+4$
View full question & answer→Question 232 Marks
Find the continues products:
$(2 p+3)(2 p-3)\left(4 p^2+9\right)$
Answer$(2 p+3)(2 p-3)\left(4 p^2+9\right)$
$\left((2 p)^2-(3)^2\right)\left(4 p^2+9\right)$
$\left(4 p^2-9\right)\left(4 p^2+9\right)$
$\left(4 p^2\right)^2-(9)^2$
$16 p^4-8$
View full question & answer→Question 242 Marks
Expand:
$(9 x-10)^2$
Answer$(9 x-10)^2$
$(9 x)^2-2 \times 9 x \times 10+(10)^2$
$=81 x^2-180 x+100$
View full question & answer→Question 252 Marks
Divide
$5 m^3-30 m^2+45 m$ by $5 m$
Answer$(5\text{m}^3 - 30\text{m}^2 + 45\text{m}) \div5\text{m}$
$=\frac{5\text{m}^3}{5\text{m}}-\frac{30\text{m}^2}{5\text{m}}+\frac{45\text{m}}{5\text{m}}$
$=\text{m}^2-6\text{m}+9$
View full question & answer→Question 262 Marks
Find the following products:
$(3 y-8) \times(5 y-1)$
Answer$(3 y-8) \times(5 y-1)$
$= 3 y(5 y-1)-8(5 y-1)$
$= 15 y^2-3 y-40 y+8$
$= 15 y^2-43 y+8$
View full question & answer→Question 272 Marks
Find the value of:
$(14.7 \times 15.3)$
Answer$(14.7 \times 15.3)$
$=(15-0.3) \times(15+0.3)$
$=(15)^2-(0.3)^2$
$=225-0.09$
$=224.91$
View full question & answer→Question 282 Marks
Find the value of the expression $\left(64 x^2+81 y^2+144 x y\right)$, when $x =11$ and $y =\frac{4}{3}$.
Answer$(64\text{x}^2 + 81\text{y}^2 + 144\text{xy})$
$=(8\text{x})^2 + (9\text{y})^2 + 2(8\text{x})(9\text{y})$
$=(8\text{x} +9\text{y} )^2 $
$=\Big(8\times11+9\times\frac{4}{3}\Big)^2$
$=(88+12)^2$
$=(100)^2$
$=10000$
View full question & answer→Question 292 Marks
Divide:
$9 x^2 y-6 x y+12 x y^2$ by $-3 x y$
Answer$\Big(9\text{x}^2\text{y} - 6\text{xy} + 12\text{xy}^2 )\div -3\text{xy}$
$\Rightarrow\frac{9\text{x}^2\text{y}}{-3\text{xy}}-\frac{6\text{xy}}{-3\text{xy}}+\frac{12\text{xy}^2}{ -3\text{xy}}$
$\Rightarrow-3\text{x} + 2 -4\text{y}$
View full question & answer→Question 302 Marks
Using the formula for squaring a binomial, evaluate the following:
$(54)^2$
Answer$(54)^2$
$=(50+4)^2$
$=(50)^2+2 \times 50 \times 4+(4)^2$
$=2500+400+16$
$=2916$
View full question & answer→Question 312 Marks
Add:
6p + 4q - r + 3, 2r - 5p - 6, 11q - 7p + 2r - 1 and 2q - 3r + 4
Question 322 Marks
Expand:
$(7 x+2 y)^2$
Answer$(7 x+2 y)^2$
$=(7 x)^2+2 \times 7 x \times 2 y+(2 y)^2$
$=49 x^2+28 x y+4 y^2$
View full question & answer→Question 332 Marks
Expand:
$\Big(\frac{\text{a}}{2}+\frac{2}{\text{a}}\Big)^2$
Answer$\Big(\frac{\text{a}}{2}+\frac{2}{\text{a}}\Big)^2$
$$$=\Big(\frac{\text{a}}2\Big)^2+2\times\frac{\text{a}}{2}×\frac{2}{\text{a}}+\Big(\frac{2}{\text{a}}\Big)2$
$=\frac{{\text{a}}^2}{4}+2+\frac{4}{\text{a}^2}$
View full question & answer→Question 342 Marks
Write the quotient and remainder when we divide:
$\left(x^2+12 x+35\right)$ by $(x+7)$
View full question & answer→Question 352 Marks
Find the value of:
$(128)^2-(72)^2$
Answer$(128)^2-(72)^2$
$=(128+72)(128-72)$
$=200 \times 56$
$=11200$
View full question & answer→Question 362 Marks
Find the following products:
$\left(2 x^2-5 y^2\right) \times\left(x^2+3 y^2\right)$
Answer$\left(2 x^2-5 y^2\right) \times\left(x^2+3 y^2\right)$
$=2 x^2\left(x^2+3 y^2\right)-5 y^2\left(x^2+3 y^2\right)$
$=2 x^4+6 x^2 y^2-5 x^2 y^2-15 y^4$
$=2 x^4+x^2 y^2-15 y^4$
View full question & answer→Question 372 Marks
The two adjacent sides of a rectangle are $5 x^2-3 y^2$ and $x^2+2 x y$. Find the perimeter.
AnswerLet legnth of rectangle $=5 x^2-3 y^2$
and breadth $=x^2+2 x y$
Perimeter $=2$ (Length + Breadth)
$=2\left(5 x^2-3 y^2+x^2+2 x y\right)$
$=2\left(6 x^2-3 y^2+2 x y\right)$
$=12 x^2-6 y^2+4 x y$
View full question & answer→Question 382 Marks
Find following products:
$\Big(5\text{x}^2+\frac{3}{4}\text{y}^2\Big)\Big(5\text{x}^2-\frac{3}{4}\text{y}^2\Big)$
Answer$\Big(5\text{x}^2+\frac{3}{4}\text{y}^2\Big)\Big(5\text{x}^2-\frac{3}{4}\text{y}^2\Big)$
$=(5\text{x}^2)^2-\Big(\frac{3}{4}\text{y}^2\Big)^2$
$=25\text{x}^4-\frac{9}{16}\text{y}^4 $
View full question & answer→Question 392 Marks
Find the value of:
$197 \times 203$
Answer$ 197 \times 203$
$= (200-3)(200+3)$
$= (200)^2-(3)^2$
$= 40000-9$
$= 39991$
View full question & answer→Question 402 Marks
Find following products:
$\Big(2\text{a}+\frac{3}{\text{b}})(2\text{a}-\frac{3}{\text{b}}\Big)$
Answer$\Big(2\text{a}+\frac{3}{\text{b}})(2\text{a}-\frac{3}{\text{b}}\Big)$
$=(2\text{a})^2-\Big(\frac{3}{\text{b}}\Big)^2$
$=4\text{a}^2-\frac{9}{\text{b}^2}$
View full question & answer→Question 412 Marks
Find the following products:
$(2 x+5) \times(4 x-3)$
Answer$(2 x+5) \times(4 x-3)$
$=2 x(4 x-3)+5(4 x-3)$
$=8 x^2-6 x+20 x-15$
$=8 x^2+14 x-15$
View full question & answer→Question 422 Marks
Find following products:
$\Big(\frac{2}{3}\text{x}+\frac{4}{5}\text{y}\Big)\Big(\frac{2}{3}\text{x}+\frac{4}{5}\text{y}\Big)$
Answer$\Big(\frac{2}{3}\text{x}+\frac{4}{5}\text{y}\Big)\Big(\frac{2}{3}\text{x}+\frac{4}{5}\text{y}\Big)$
$=\Big(\frac{2}{3}\text{x}+\frac{4}{5}\text{y}\Big)^2$
$=\Big(\frac{2}{3}\text{x}\Big)^2+\Big(\frac{4}{5}\text{y}\Big)^2+2×\frac{2}{3}\text{x}×\frac{4}{5}\text{y} $
$=\frac{4}{9}\text{x}^2+\frac{16}{25}\text{y}^2+\frac{16}{15}\text{xy}$
View full question & answer→Question 432 Marks
Write the quotient and remainder when we divide:
$\left(14 x^2-53 x+45\right) \text { by }(7 x-9)$
View full question & answer→Question 442 Marks
Find the continues products:
$(3 x-2 y)(3 x+2 y)\left(9 x^2+4 y^2\right)$
Answer$(3 x-2 y)(3 x+2 y)\left(9 x^2+4 y^2\right)$
$=\left((3 x)^2-(2 y)^2\right)\left(9 x^2+4 y^2\right)$
$=\left(9 x^2-4 y^2\right)\left(9 x^2+4 y^2\right)$
$=\left(9 x^2\right)^2-\left(4 y^2\right)^2$
$=81 x^4-16 y^4$
View full question & answer→Question 452 Marks
Find the following products:
$\left(9 x^2-x+15\right) \times\left(x^2-3\right)$
Answer$\left(9 x^2-x+15\right) \times\left(x^2-3\right)$
$=\left(9 x^2-x+15\right) \times x^2\left(9 x^2-x+15\right) \times(-3)$
$=9 x^4-x^3+15 x^2-27 x^2+3 x-45$
$=9 x^4-x^3-12 x^2+3 x-45$
View full question & answer→Question 462 Marks
Add:
5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x -2z - 3y
Question 472 Marks
Find following products:
$\Big(\frac{4\text{x}}{5}-\frac{5\text{y}}{3}\Big)\Big(\frac{4\text{x}}{5}+\frac{5\text{y}}{3}\Big)$
Answer$\Big(\frac{4\text{x}}{5}-\frac{5\text{y}}{3}\Big)\Big(\frac{4\text{x}}{5}+\frac{5\text{y}}{3}\Big)$
$=(5\text{x}^2)^2-\Big(\frac{3}{4}\text{y}^2\Big)^2$
$=\frac{16}{25}\text{x}^2-\frac{25}{9}\text{y}^2$
View full question & answer→Question 482 Marks
Find the following products:
$\left(x^3-2 x^2+5\right) \times(4 x-1)$
Answer$=\left(x^3-2 x^2+5\right) \times 4 x+1\left(x^3-2 x^2+5\right) \times(-1)$
$=4 x^4-8 x^3+20 x-x^3+2 x^3-5$
$=4 x^4-9 x^3+2 x^2+20 x-5$
View full question & answer→Question 492 Marks
Find the following products:
$(4 x+9) \times(x-6)$
Answer$(4 x+9) \times(x-6)$
$=4 x(x-6)+9(x-6)$
$=4 x^2-24 x+9 x-54$
$=4 x^2-15 x-54$
View full question & answer→Question 502 Marks
Find the following products:
$(3 m-4 n) \times(2 m-3 n)$
Answer$(3 m-4 n) \times(2 m-3 n)$
$= 3 m(2 m-3 n)-4 n(2 m-3 n)$
$= 6 m^2-9 m n-8 m n+12 n^2$
$= 6 m^2-17 m n+12 n^2$
View full question & answer→Question 512 Marks
Subtract:
$x^3+3 x^2-5 x+4$ from $3 x^3-x^2+2 x-4$
View full question & answer→Question 522 Marks
Add $: 3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c$
AnswerWriting the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
$3 a-4 b+4 c$
$2 a+3 b-8 c$
$a-6 b+c$
$\overline{6 a-7 b-3} c$
View full question & answer→Question 532 Marks
Find the continues products:
$(x-3)(x+3)\left(x^2+9\right)$
Answer$(x-3)(x+3)\left(x^2+9\right)$
$=\left\{(x)^2-(3)^2\right\}\left(x^2+9\right)$
$=\left(x^2-9\right)\left(x^2+9\right)$
$=\left(x^2\right)^2-(9)^2$
$=x^4-81$
View full question & answer→Question 542 Marks
Subtract:
What must be subtracted from $3 a^2-6 a b-3 b^2-1$ to get $4 a^2-7 a b-4 b^2+1$ ?
View full question & answer→Question 552 Marks
Find the following products:
$\left(x^3-5 x^2+3 x+1\right) \times\left(x^3-3\right)$
Answer$\left(x^3-5 x^2+3 x+1\right) \times\left(x^3-3\right)$
$=x^2\left(x^3-5 x^2+3 x+1\right)-3\left(x^3-5 x^2+3 x+1\right)$
$=x^5-5 x^4+3 x^3+x^2-3 x^3+15 x^2-9 x-3$
$=x^5-5 x^4+16 x^2-9 x-3$
View full question & answer→Question 562 Marks
Find the value of expression $\left(36 x^2+25 y^2-60 x y\right)$, when $x =\frac{2}{3}$ and $y =\frac{1}{5}$.
Answer$(36\text{x}^2 + 25\text{y}^2 - 60\text{xy})$
$= (6\text{x})^2 + (5\text{y})^2 - 2 × 6\text{x} × 5\text{y}$
$= (6\text{x} - 5\text{y})^2$
$=\Big(6\times\frac{2}{3}-5\times\frac{1}{5}\Big)^2$
$=(4-1)^2$
$=(3)^2=9$
View full question & answer→Question 572 Marks
Write the quotient and remainder when we divide:
$\left(15 x^2+x-6\right)$ by $(3 x+2)$
View full question & answer→Question 582 Marks
The perimeter of a triangle is $6 p^2-4 p+9$ and two of its sides are $p^2-2 p+1$ and $3 p^2-5 p+3$. Find the third side of the triangle.
AnswerPerimeter of triangle $=6 p^2-4 p+9$
Sum of two sides of it $=3 p^2-5 p+3+p^2-2 p+1$
$=4 p^2-7 p-4$
$\text { Third side }=\left(6 p^2-4 p+9\right)-\left(4 p^2+7 p-4\right)$
$=6 p^2-4 p+9-4 p^2+7 p-4$
$=2 p^2+3 p+5$
View full question & answer→Question 592 Marks
Find the following products:
$\left(3 p^2+q^2\right) \times\left(2 p^2-3 q^2\right)$
Answer$\left(3 p^2+q^2\right) \times\left(2 p^2-3 q^2\right)$
$=3 p^2\left(2 p^2-3 q^2\right)+q^2\left(2 p^2-3 q^2\right)$
$=6 p^4-9 p^2 q^2+2 p^2 q^2-3 q 4$
$=6 p^4-7 p^2 q^2-3 q^4$
View full question & answer→Question 602 Marks
Using the formula for squaring a binomial, evaluate the following:
$(82)^2$
Answer$(82)^2$
$=(80+2)^2$
$=(80)^2+2 \times 80 \times 2+(2)^2$
$=6400+320+4$
$=6724$
View full question & answer→Question 612 Marks
Write the quotient and remainder when we divide:
$\left(6 x^2-31 x+47\right)$ by $(2 x-5)$
View full question & answer→Question 622 Marks
Using the formula for squaring a binomial, evaluate the following:
$(69)^2$
Answer$(69)^2$
$=(70-1)^2$
$=(70)^2-2 \times 70 \times 1+(1)^2$
$=4900-140+1$
$=4901-140$
$=4761$
View full question & answer→Question 632 Marks
Using the formula for squaring a binomial, evaluate the following:
$(103)^2$
Answer$(103)^2$
$= (100+3)^2$
$= (100)^2+2 \times 100 \times 3+(3)^2$
$= 10000+600+9$
$= 10609$
View full question & answer→Question 642 Marks
Find the following products:
$\left(x^2-a^2\right) \times(x-a)$
Answer$\left(x^2-a^2\right) \times(x-a)$
$=x^2(x-a)-a^2(x-a)$
$=x^3-a x^2-a^2 x+a^3$
View full question & answer→Question 652 Marks
Find the value of:
$\frac{198\times198-102\times102}{96}$
Answer$\frac{198\times198-102\times102}{96}$
$=\frac{(198)^2-(102)^2}{96}$
$=\frac{(198-102)(198+102)}{96}$
$=\frac{300\times96}{96}$
$=300$
View full question & answer→Question 662 Marks
Find following products:
$\Big(\text{x}+\frac{1}{\text{x}}\Big)\Big(\text{x}-\frac{1}{\text{x}}\Big)$
Answer$\Big(\text{x}+\frac{1}{\text{x}}\Big)\Big(\text{x}-\frac{1}{\text{x}}\Big)$$=(\text{x})^2-\Big(\frac{1}{\text{x}}\Big)^2$
$\text{x}^2-\frac{1}{\text{x}^2}$
View full question & answer→Question 672 Marks
Find following products:
$(4 x+5 y)(4 x+5 y)$
Answer$(4 x+5 y)(4 x+5 y)$
$=(4 x+5 y)^2$
$=(4 x)^2+2 \times 4 x \times 5 y+(5 y)^2$
$=16 x^2+25 y^2+40 x y$
View full question & answer→Question 682 Marks
Expand:
$(8 a+3 b)^2$
Answer$(8 a +3 b)^2$
$=(8 a)^2+2 \times 8 a \times 3 b+(3 b)^2$
$=64 a^2+48 a b+9 b^2$
View full question & answer→Question 692 Marks
Divide:
$12 x ^4+8 x ^3-6 x ^2 \text { by }-2 x ^2$
Answer$\Big(12\text{x}^4 + 8\text{x}^3 - 6\text{x}^2 \Big)\div -2\text{x}^2$
$\Rightarrow\frac{12\text{x}^4}{ -2\text{x}^2}+\frac{8\text{x}^3}{-\text{2x}^2}-\frac{6\text{x}^2}{-2\text{x}^2}$
$\Rightarrow−6\text{x} $
View full question & answer→Question 702 Marks
Write the quotient and remainder when we divide:
$\left(x^3+1\right)$ by $(x+1)$
View full question & answer→Question 712 Marks
Expand:
$\Big(3\text{m}-\frac{4}{5}\text{n}\Big)^2$
Answer$\Big(3\text{m}-\frac{4}{5}\text{n}\Big)^2$
$=\Big(\text{3m}\Big)^2-2\times3\text{m}\times\frac{4}{5}\text{n}+\Big(\frac{4}{5}\text{n}\Big)^2$
$=9\text{m}^2-\frac{24\text{mn}}{5}+\frac{16}{25}\text{n}^2$
View full question & answer→Question 722 Marks
Divide
$8 x^2 y^2-6 x y^2+10 x^2 y^3 \text { by } 2 x y$
Answer$(8\text{x}^2\text{y}^2 − 6\text{xy}^2 + 10\text{x}^2\text{y}^3 )\div 2\text{xy}$
$\Rightarrow\frac{8\text{x}^2\text{y}^2}{2\text{xy}}− \frac{6\text{xy}^2}{2\text{xy}}+ \frac{10\text{x}^2\text{y}^3}{ 2\text{xy }}$
$\Rightarrow4\text{xy} - 3\text{y} + 5\text{xy}^2$
View full question & answer→Question 732 Marks
Find following products:
$\left(x^2+7\right)\left(x^2+7\right)$
Answer$\left(x^2+7\right)\left(x^2+7\right)$
$=\left(x^2+7\right)^2$
$=\left(x^2\right)^2+7^2+2 \times x^2 \times 7$
$=x^4+49+14 x^2$
View full question & answer→Question 742 Marks
Subtract:
2a - 5b + 2c - 9 from 3a - 4b - c + 6
Question 752 Marks
Find the following products:
$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$
Answer$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$
$=\left(x^2-5 x+8\right) \times x^2+\left(x^2-5 x+8\right) \times 2$
$=x^4-5 x^3+8 x^2+2 x^2-10 x+16$
$=x^4-5 x^3+10 x^2-10 x+16$
View full question & answer→Question 762 Marks
Add:
7x, -3x, 5x, -x, -2x
Answer7x + (-3x) + 5x + (-x) + (-2x)
= 7x - 3x + 5x - x - 2x
= 12x - 6x = 6x
View full question & answer→Question 772 Marks
Add:
$2 x^3-9 x^2+8,3 x^2-6 x-5,7 x^3-10 x+1$ and $3+2 x-5 x^2-4 x^3$
View full question & answer→Question 782 Marks
Add: $4 x^2-7 x y+4 y^2-3,5+6 y^2-8 x y+x^2$ and $6-2 x y+2 x^2-5 y^2$
Answer$4 x^2+4 y^2-7 x y-3$
$x^2+6 y^2-8 x y+5$
$\underline {2 x^2-5 y^2-2 x y+6}$
$7 x^2+5 y^2-17 x y+8$
View full question & answer→Question 792 Marks
Find the following products:
$\left(3 x^2+5 x-9\right) \times(3 x-5)$
Answer$\left(3 x^2+5 x-9\right) \times(3 x-5)$
$=3 x^2(3 x-5 x)+5 x(3 x-5)-9(3 x-5)$
$=9 x^3+15 x^2-27 x-15 x^2-25 x+45$
$=9 x^3-52 x+45$
View full question & answer→Question 802 Marks
Subtract:
$5 y^4-3 y^3+2 y^2+y-1$ from $4 y^4-2 y^3-6 y^2-y+5$
View full question & answer→Question 812 Marks
Find following products:
$(x-4)(x-4)$
Answer$(x-4)(x-4)$
$=(x-4)^2$
$=(x)^2-2 \times x \times 4+(4)^2$
$=x^2-8 x+16$
View full question & answer→Question 822 Marks
Find the following products:
$\left(x^4+y^4\right) \times\left(x^2-y^2\right)$
Answer$\left(x^4+y^4\right) \times\left(x^2-y^2\right)$
$=x^4\left(x^2-y^2\right)+y^4\left(x^2-y^2\right)$
$=x^6-x^4 y^2+x^2 y^4-y^6$
View full question & answer→Question 832 Marks
Find the following products:
$\left(x^3-y^3\right) \times\left(x^2+y^2\right)$
Answer$\left(x^3-y^3\right) \times\left(x^2+y^2\right)$
$=x^3\left(x^2+y^2\right)-y^3\left(x^2+y^2\right)$
$=x^5+x^3 y^2-x^2 y^3-y^5$
View full question & answer→Question 842 Marks
Find the following products:
$\left(x^2-y^2\right) \times(x+2 y)$
Answer$\left(x^2-y^2\right) \times(x+2 y)$
$=x^2(x+2 y)-y^2(x+2 y)$
$=x^3+2 x^2 y-x y^2-2 y^3$
View full question & answer→Question 852 Marks
Find following products:
$(7 a+9 b)(7 a+9 b)$
Answer$=(7 a+9 b)^2$
$=(7 a)^2+(9 b)^2+2 \times 7 a \times 9 b$
$=49 a^2+81 b^2+126 a b$
View full question & answer→Question 862 Marks
Find the value of the expression $\left(9 x^2+24 x+16\right)$, when $x=12$.
Answer$\left(9 x^2+24 x+16\right)$
$=(3 x)^2+2(3 x)(4)+(4)$
$=(3 x+4)^2$
$=(3 \times 12+4)^2$
$=(36+4)^2$
$=(40)^2$
$=1600$
View full question & answer→Question 872 Marks
Find the following products:
$(9 x+5 y) \times(4 x+3 y)$
Answer$(9 x+5 y) \times(4 x+3 y)$
$9 x(4 x+3 y)+5 y(4 x+3 y)$
$=36 x^2+27 x y+20 x y+15 y^2$
$=36 x^2+47 x y+15 y^2$
View full question & answer→Question 882 Marks
Subtract:
$4 p^2+5 q^2-6 r^2+7$ from $3 p^2-4 q^2-5 r^2-6$
View full question & answer→