Question 12 Marks
Using the formula for squaring a binomial, evaluate the following:
$ (197)^2$
Answer$(197)^2$
$= (200 - 3)^2$
$= (200)^2- 2 × 200 × 3 + (3)^2$
$= 40000 - 1200 + 9$
$= 40009 - 1200$
$= 38809$
View full question & answer→Question 22 Marks
Find the following products:$ (7x + 2y) × (x + 4y)$
Answer$(7x + 2y) × (x + 4y)$
$= 7x(x + 4y) + 2y(x + 4y)$
$ =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 \times 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$(78)^2$
$= (80 - 2)^2$
$= (80)^2- 2 × 80 × 2 + (2)^2$
$= 6400 - 320 + 4$
$= 6404 - 320$
$= 6084$
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$(999)^2$
$= (1000 - 1)^2$
$= (1000)^2- 2 × 1000 × 1 + (1)^2$
$= 1000000 - 2000 + 1$
$= 1000001 - 2000$
$= 998001$
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 × 7.26$
$ = 72.6$
View full question & answer→Question 102 Marks
Find following products:
$ (2x - 3y)(2x - 3y)$
Answer$(2x - 3y)(2x - 3y)$
$ =(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 112 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.=\left\{(x)^2-(1)^2\right\} 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 122 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 132 Marks
Find the following products:
$ \left(x^2-x y+y^2\right) x(x+y) $
Answer$ \left(x^2-x y+y^2\right) x(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 142 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 152 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 162 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 172 Marks
Find the following product: $(3x + 2y - 4) × (x - y + 2)$
View full question & answer→Question 182 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 192 Marks
Expand:
$(5x + 11)^2$
Answer$(5x + 11)^2$
$= (5x)^2+ 2 × 5x × 11 + (11)^2$
$= 25x^2+ 110x + 121$
View full question & answer→Question 202 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 212 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^4-81 $
View full question & answer→Question 222 Marks
Expand:
$(9x - 10)^2$
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 232 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 242 Marks
Find the following products:
$(3y - 8) × (5y - 1)$
Answer$(3y - 8) × (5y - 1)$
$= 3y(5y - 1) - 8(5y - 1)$
$ =15 y^2-3 y-40 y+8 $
$ =15 y^2-43 y+8 $
View full question & answer→Question 252 Marks
Find the value of:
$ (14.7 × 15.3)$
Answer$(14.7 × 15.3)$
$= (15 - 0.3) × (15 + 0.3)$
$= (15)^2- (0.3)^2$
$= 225 - 0.09$
$= 224.91$
View full question & answer→Question 262 Marks
Find the value of the expression $(64\text{x}^2 + 81\text{y}^2 + 144\text{xy})$, when $\text{x} = 11$ and $\text{y}=\frac{4}{3}.$
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 272 Marks
Divide: $9 x^2 y-6 x y+12 x y^2$ by $-3 x y$
View full question & answer→Question 282 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 292 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 302 Marks
Expand: $\Big(\frac{\text{a}}{2}+\frac{2}{\text{a}}\Big)^2$
Answer$\Big(\frac{\text{a}}{2}+\frac{2}{\text{a}}\Big)^2$
$=\Big(\frac{\text{a}}2\Big)^2+2\times\frac{\text{a}}{2}\times \frac{2}{\text{a}}+\Big(\frac{2}{\text{a}}\Big)2$
$=\frac{{\text{a}}^2}{4}+2+\frac{4}{\text{a}^2}$
View full question & answer→Question 312 Marks
Write the quotient and remainder when we divide:
$\left(x^2+12 x+35\right)$ by $(x+7)$
View full question & answer→Question 322 Marks
Find the value of:
$(128)^2- (72)^2$
Answer$(128)^2- (72)^2$
$= (128 + 72)(128 - 72)$
$= 200 × 56$
$= 11200$
View full question & answer→Question 332 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 342 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 $= 5x^2- 3y^2$
and breadth $= x^2+ 2xy$
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 352 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 362 Marks
Find the value of:
$197 × 203$
Answer$197 × 203$
$= (200 - 3)(200 + 3)$
$= (200)^2- (3)^2$
$= 40000 - 9$
$= 39991$
View full question & answer→Question 372 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 382 Marks
Find the following products:
$ (2x + 5) × (4x - 3)$
Answer$(2x + 5) × (4x - 3)$
$= 2x(4x - 3) + 5(4x - 3)$
$= 8x^2- 6x + 20x - 15$
$= 8x^2+ 14x - 15$
View full question & answer→Question 392 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 402 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 412 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 422 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 432 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 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 442 Marks
Find the following products:
$ (4x + 9) × (x - 6)$
Answer$(4x + 9) × (x - 6)$
$= 4x(x - 6) + 9(x - 6)$
$= 4x^2- 24x + 9x - 54$
$= 4x^2- 15x - 54$
View full question & answer→Question 452 Marks
Find the following products:
$(3m - 4n) × (2m - 3n)$
Answer$(3m - 4n) × (2m - 3n)$
$= 3m(2m - 3n) - 4n(2m - 3n)$
$ =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 462 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 472 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 482 Marks
Find the value of expression $(36x^2+ 25y^2- 60xy),$ When $\text{x}=\frac{2}{3}$ and $\text{y}=\frac{1}{5}.$
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 492 Marks
The perimeter of a triangle is $6p^2- 4p + 9$ and two of its sides are $p^2- 2p + 1$ and $3p^2- 5p + 3.$ Find the third side of the triangle.
AnswerPerimeter of triangle $= 6p^2- 4p + 9$
Sum of two sides of it $= 3p^2- 5p + 3 + p^2- 2p + 1$
$= 4p^2- 7p - 4$
Third side $= (6p^2- 4p + 9) - (4p^2+ 7p - 4)$
$= 6p^2- 4p + 9 - 4p^2+ 7p - 4$
$= 2p^2+ 3p + 5$
View full question & answer→Question 502 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→