Question 13 Marks
Simplify: $\mathrm{x}-(3 \mathrm{y}-\overline{4 \mathrm{x}-3 \mathrm{x}}+2 z-\overline{5 \mathrm{y}-7 \mathrm{x}})$
Answer
$\begin{aligned} & x-(3 y-\overline{4 x-3 x}+2 z-\overline{5 y-7 x}) \\ & =x-(3 y-4 z+3 x+2 z-5 y+7 x) \\ & =x-(-2 y-2 z+10 x) \\ & =x+2 y+2 z-10 x \\ & =-9 x+2 y+2 z\end{aligned}$
View full question & answer→Question 23 Marks
Simplify: -1[a - 3{b - 4(a - b - 8) + 4a} + 10]
Answer-1[a - 3{b - 4(a - b - 8) + 4a} + 10]
= -1[a - 3{b - 4a + 4b + 32 + 4a} + 10]
= -1[a - 3{5b + 32} + 10]
= -1[a - 15b - 96 + 10]
= -1[a - 15b - 86]
= -a + 15b + 86
View full question & answer→Question 33 Marks
Simplify: 9x + 5 – [4x – {3x – 2 (4x – 3)}]
Answer9x + 5 – [4x – {3x – 2 (4x – 3)}]
= 9x + 5 – [4x – {3x – 8x + 6}]
= 9x + 5 – [4x – 3x + 8x – 6]
= 9x + 5-4x + 3x - 8x + 6
= 9x + 3x - 4x - 8x + 5 + 6
= 12x - 12x + 11
= 11
View full question & answer→Question 43 Marks
Simplify: 2 [a – 3 {a + 5 {a – 2) + 7}]
Answer2 [a – 3 {a + 5 {a – 2) + 7}]
= 2 [a - 3 {a + 5a - 10 + 7}]
= 2 [a - 3a - 15a + 30 - 21]
= 2a - 6a - 30a + 60 - 42
= 2a - 36a + 60 - 42
= -34a + 18
View full question & answer→Question 53 Marks
Simplify: 2x-[5y- (3x -y) + x]
Answer2x - [5y - (3x - y) + x]
= 2x – {5y – 3x +y + x}
= 2x – 5y + 3x -y – x
= 2x + 3x – x – 5y – y
= 4x – 6y
View full question & answer→Question 63 Marks
Simplify: 3x + [4x – (6x – 3)]
Answer3x + [4x – (6x – 3)]
= 3x + [4x – 6x + 3]
= 3x + 4x – 6x + 3
= 3x + 4x – 6x + 3
= 7x – 6x + 3
= x + 3
View full question & answer→Question 73 Marks
Simplify: $b\left(2 b-\frac{1}{b}\right)-2 b\left(b-\frac{1}{b}\right)$
Answer
$\begin{aligned} & b\left(2 b-\frac{1}{b}\right)-2 b\left(b-\frac{1}{b}\right) \\ & =b \times 2 b-b \times \frac{1}{b}-2 b \times b+2 b \times \frac{1}{b} \\ & =2 b^2-1-2 b^2+2 \\ & =2 b^2-2 b^2-1+2 \\ & =1\end{aligned}$
View full question & answer→Question 83 Marks
Simplify: $\left(\frac{y}{6}+\frac{2 y}{3}\right) \div\left(y+\frac{2 y-1}{3}\right)$
Answer
$\begin{aligned} & \left(\frac{y}{6}+\frac{2 y}{3}\right) \div\left(y+\frac{2 y-1}{3}\right) \\ & =\left(\frac{y+4 y}{6}\right) \div\left(\frac{3 y+2 y-1}{3}\right) \\ & =\frac{5 y}{6} \div \frac{5 y-1}{3} \\ & =\frac{5 y}{6} \times \frac{3}{5 y-1} \\ & =\frac{5 y}{2(5 y-1)}=\frac{5 y}{10 y-2}\end{aligned}$
View full question & answer→Question 93 Marks
Simplify: $\left(\frac{5 \mathrm{k}}{8}-\frac{3 \mathrm{k}}{5}\right) \div \frac{\mathrm{k}}{4}$
Answer
$\begin{aligned} & \left(\frac{5 \mathrm{k}}{8}-\frac{3 \mathrm{k}}{5}\right) \div \frac{\mathrm{k}}{4} \\ & =\frac{25 \mathrm{k}-24 \mathrm{k}}{40} \div \frac{\mathrm{k}}{4} \\ & =\frac{\mathrm{k}}{40} \div \frac{\mathrm{k}}{4} \\ & =\frac{\mathrm{k}}{40} \times \frac{4}{\mathrm{k}}=\frac{1}{10}\end{aligned}$
View full question & answer→Question 103 Marks
Simplify: $\left(2 p+\frac{p}{7}\right) \div\left(\frac{9 p}{10}+4 p\right)$
Answer
$\begin{aligned} & \left(2 \mathrm{p}+\frac{\mathrm{p}}{7}\right) \div\left(\frac{9 \mathrm{p}}{10}+4 \mathrm{p}\right) \\ & =\frac{14 \mathrm{p}+\mathrm{p}}{7} \div \frac{9 \mathrm{p}+40 \mathrm{p}}{10} \\ & =\frac{15}{7} \mathrm{p} \div \frac{49}{10} \mathrm{p} \\ & =\frac{15}{7} \mathrm{p} \times \frac{10}{49 \mathrm{p}} \\ & =\frac{150}{343}\end{aligned}$
View full question & answer→Question 113 Marks
Simplify: $\left(\mathrm{p}+\frac{\mathrm{p}}{3}\right)\left(2 \mathrm{p}+\frac{\mathrm{p}}{2}\right)\left(3 \mathrm{p}-\frac{2 \mathrm{p}}{3}\right)$
Answer
$\begin{aligned} & \left(p+\frac{p}{3}\right)\left(2 p+\frac{p}{2}\right)\left(3 p-\frac{2 p}{3}\right) \\ & =p\left(1+\frac{1}{3}\right) p\left(2+\frac{1}{2}\right) p\left(3-\frac{2}{3}\right) \\ & =p^3\left(\frac{3+1}{3}\right)\left(\frac{4+1}{2}\right)\left(\frac{9-2}{3}\right) \\ & =p^3 \times \frac{4}{3} \times \frac{5}{2} \times \frac{7}{3} \\ & =p^3 \times \frac{70}{9}=\frac{70 p^3}{9}\end{aligned}$
View full question & answer→Question 123 Marks
Simplify: $\frac{5(\mathrm{x}-4)}{3}+\frac{2(5 x-3)}{5}+\frac{6(x-4)}{7}$
Answer
$\begin{aligned} & \frac{5(\mathrm{x}-4)}{3}+\frac{2(5 x-3)}{5}+\frac{6(x-4)}{7} \\ & =\frac{175(\mathrm{x}-4)+42(\mathrm{x}-3)+90(\mathrm{x}-4)}{105} \ldots(\text { LCM of } 3,5,7=105) \\ & =\frac{175 \mathrm{x}-700+210 \mathrm{x}-126+90 \mathrm{x}-360}{105} \\ & =\frac{175 \mathrm{x}+210 \mathrm{x}+90 \mathrm{x}-700-126-360}{105} \\ & =\frac{475 \mathrm{x}-1186}{105}\end{aligned}$
View full question & answer→Question 133 Marks
Simplify: $\frac{y}{5}+y-\frac{19 y}{15}$
Answer
$\begin{aligned} & \frac{y}{5}+y-\frac{19 y}{15} \\ & =\frac{y}{5}+\frac{y}{1}-\frac{19 y}{15} \\ & =\frac{3 y+15 y-19 y}{15} \\ & =\frac{18 y-19 y}{15} \\ & =\frac{-y}{15}\end{aligned}$
View full question & answer→Question 143 Marks
Divide: $m^3 - 4m^2 + m + 6 by m^2 - m - 2$
View full question & answer→Question 153 Marks
Divide: $x^3 - 6x^2 + 11x - 6 by x^2 - 4x + 3$
View full question & answer→Question 163 Marks
Divide: $6x^2 - xy - 35y^2$ by $2x - 5y$
View full question & answer→Question 173 Marks
Divide: $12a^2 + ax - 6x^2$ by $3a - 2x$
View full question & answer→Question 183 Marks
Divide: $6x^3 + 5x^2 - 21x + 10$ by $3x - 2$
View full question & answer→Question 193 Marks
Divide: $35a^3 + 3a^2b - 2ab^2$ by $5a - b$
View full question & answer→Question 203 Marks
Divide: $15x^2 + 31xy + 14y^2$ by $5x + 7y$
View full question & answer→Question 213 Marks
Divide: $9x^2 - 24xy + 16y^2$ by $3x- 4y$
View full question & answer→Question 223 Marks
Divide: $8a^2 + 4a - 60$ by $2a - 5$
View full question & answer→Question 233 Marks
Divide: $6x^2 + 5x - 6$ by $2x + 3$
View full question & answer→Question 243 Marks
Divide: $2a^2 - 11a + 12$ by $a - 4$
View full question & answer→Question 253 Marks
Divide: $x^2 + 4xy + 4y^2 by x + 2y$
View full question & answer→Question 263 Marks
Divide: $p^2 + 4p + 4 by p + 2$
View full question & answer→Question 273 Marks
Divide: $4a^2 + 4a + 1$ by $2a + 1$
AnswerSolution is as follow:
View full question & answer→Question 283 Marks
Divide: $m^2 - 2mn + n^2 by m - n$
Answer
$m^2-2 m n+n^2$ by $m-n$
View full question & answer→Question 293 Marks
Divide: $n^2 - 2n + 1$ by $n - 1$
Answer
$n^2-2 n+1$ by $n-1$
View full question & answer→Question 303 Marks
Divide: $9a^4b - 15a^3b^2 + 12a^2b^3 by - 3a^2b$
Answer$9 a^4 b-15 a^3 b^2+12 a^2 b^3 b y-3 a^2 b$
$=\frac{9 a^4 b-15 a^3 b^2+12 a^2 b^3}{-3 a^2 b}$
$=\frac{9 a^4}{-3 a^2 b}-\frac{15 a^3 b^2}{-3 a^2 b}+\frac{12 a^2 b^3}{-3 a^2 b}$
$=-3 a^2+5 a b-4 b^2$
View full question & answer→Question 313 Marks
Divide: $12x^3y - 8x^2y^2 + 4x^2y^3 by 4xy$
Answer$12 x^3 y-8 x^2 y^2+4 x^2 y^3 \text { by } 4 x y $
$=\frac{12 x^3 y-8 x^2 y^2+4 x^2 y^3}{4 x y} $
$=\frac{12 x^3 y}{4 x y}-\frac{8 x^2 y^2}{4 x y}+\frac{4 x^2 y^3}{4 x y} $
$=3 x^2-2 x y+x y^2$
View full question & answer→Question 323 Marks
Divide: $10a^3 - 15a^2b$ by $- 5a^2$
Answer$10a^3 - 15a^2b$ by $- 5a^2$
$=\frac{10 a^3-15 a^2 b}{-5 a^2} $
$=\frac{10 a^3}{-5 a^2} $
$=\frac{15 a^2 b}{-5 a^2} $
$=-2 a+3 b$
View full question & answer→Question 333 Marks
Multiply: $(1 + 6x^2 - 4x^3)(-1 + 3x - 3x^2)$
Answer$(1 + 6x^2 - 4x^3)(-1 + 3x - 3x^2)$
$\Rightarrow 1(- 1 + 3x - 3x^2) + 6x^2 (- 1 + 3x - 3x^2) - 4x^3 (- 1 + 3x - 3x^2)$
$\Rightarrow - 1 + 3x - 3x^2 - 6x^2 + 18x^3 - 18x^4 + 4x^3 - 12x^4 + 12x^5$
$\Rightarrow - 1 + 3x - 9x^2 + 22x^3 - 30x^4 + 12x^5$
View full question & answer→Question 343 Marks
Multiply: $(3x - 5y + 2)(5x - 4y - 3)$
Answer$(3x - 5y + 2)(5x - 4y - 3)$
$\Rightarrow 3x (5x - 4y - 3) - 5y (5x - 4y - 3) + 2 (5x - 4y - 3)$
$\Rightarrow 15x^2 - 12xy - 9x - 25xy + 20y^2 + 15y + 10x - 8y - 6$
$\Rightarrow 15x^2 - 12xy - 25xy - 9x + 10x + 20y^2 + 15y - 8y - 6$
$\Rightarrow 15x^2 - 37xy + x + 20y^2 + 7y - 6$
View full question & answer→Question 353 Marks
Multiply:$ (2x + 5y + 6)(3x + y - 8)$
Answer$(2x + 5y + 6)(3x + y - 8)$
$\Rightarrow 2x (3x + y - 8) + 5y(3x + y - 8) + 6 (3x + y - 8)$
$\Rightarrow 6x^2 + 2xy - 16x + 15xy + 5y^2 - 40y + 18x + 6y - 48$
$\Rightarrow 6x^2 + 2xy + 15xy - 16x + 18x + 5y^2 - 40y + 6y - 48$
$\Rightarrow 6x^2 + 17xy + 2x + 5y^2 - 34y - 48$
View full question & answer→Question 363 Marks
Multiply: $(2x - 3y)(2x - 3y)$
Answer$(2x - 3y)(2x - 3y)$
$\Rightarrow 2x (2x - 3y) - 3y(2x - 3y)$
$\Rightarrow 2x \times 2x - 2x \times 3y + 3y \times 2x + 3y \times 3y$
$\Rightarrow 4x^2 - 6xy - 6xy + 9y^2$
$\Rightarrow 4x^2 - 12xy + 9y^2$
View full question & answer→Question 373 Marks
Multiply: $(2x + 3y)(2x - 3y)$
Answer$(2x + 3y)(2x - 3y)$
$\Rightarrow 2x (2x - 3y) + 3y(2x - 3y)$
$\Rightarrow 2x \times 2x - 2x \times 3y + 3y \times 2x - 3y \times 3y$
$\Rightarrow 4x^2 - 6xy + 6xy - 9y^2$
$\Rightarrow 4x^2 - 0 - 9y^2$
$\Rightarrow 4x^2 - 9y^2$
View full question & answer→Question 383 Marks
Multiply: $(2x - 3y)(2x + 3y)$
Answer$(2x - 3y)(2x + 3y)$
$\Rightarrow 2x (2x + 3y) - 3y(2x + 3y)$
$\Rightarrow 2x \times 2x + 2x \times 3y - 3y \times 2x - 3y \times 3y$
$\Rightarrow 4x^2 + 6xy - 6xy - 9y^2$
$\Rightarrow 4x^2 + 0 - 9y^2$
$\Rightarrow 4x^2 - 9y^2$
View full question & answer→Question 393 Marks
Evaluate:$ - 4y (15 + 12y - 8z) (x - 2y)$
Answer$- 4y (15 + 12y - 8z) (x - 2y)$
$= - 4y (x - 2y)(15x + 12y - 8z)$
$= (- 4xy + 8y^2)(15x + 12y - 8z)$
$= - 4xy (15x + 12y - 8z) + 8y^2 (15x +12y - 8z)$
$= -60x^2y - 48xy^2 + 32xy + 120xy^2 + 96y^3 - 64y^2z$
$= -60x^2y - 48xy^2 + 120xy^2 - 64y^2z + 96y^3 + 32xy$
$= -60x^2y + 72xy2 - 64y^2z + 96y^3 + 32xyz$
View full question & answer→Question 403 Marks
Evaluate: $(4x^2 - 4x + 1)(2x^3 - 3x^2 + 2)$
Answer$(4x^2 - 4x + 1)(2x^3 - 3x^2 + 2)$
$= 4x^2 (2x^3 - 3x^2 + 2) - 4x (2x^3 - 3x^2 + 2) + 1 (2x^3 - 3x^2 + 2)$
$= 8x^5 - 12x^4 + 8x^2 - 8x^4 + 12x^3 - 8x + 2x^3 - 3x^2 + 2$
$= 8x^5 - 12x^4 - 8x^4 + 12x^3 + 2x^3 + 8x^2 - 3x^2 - 8x + 2$
$= 8x^5 - 20x^4 + 14x^3 + 5x^2 - 8x + 2$
View full question & answer→Question 413 Marks
Evaluate: $(8 - 12x + 7x^2 - 6x^3)(5 - 2x)$
Answer$(8 - 12x + 7x^2 - 6x^3)(5 - 2x)$
$= 5(8 - 12x + 7x^2 - 6x^3) - 2x (8 - 12x + 7x^2 - 6x^3)$
$= 40 - 60x + 35x^2 - 30x^3 - 16x + 24x^4 - 14x^3 + 12x^4$
$= 40 - 60x - 16x + 35x^2 + 24x^4 - 30x^3 - 14x^3 + 12x^4$
$= 40 - 76x + 59x^2 - 44x^3 + 12x^4$
View full question & answer→Question 423 Marks
Evaluate: $(4m - 2)(m^2 + 5m - 6)$
Answer$(4m - 2)(m^2 + 5m - 6)$
$= 4m (m^2 + 5m - 6) - 2(m^2 + 5m - 6)$
$= 4m^3 + 20m^2 - 24m - 2m^2 - 10m + 12$
$= 4m^3 + 20m^2 - 2m^2 - 24m - 10m + 12$
$= 4m^3 + 18m^2 - 34m + 12$
View full question & answer→Question 433 Marks
Evaluate:$ (3x - 1)(4x^3 - 2x^2 + 6x - 3)$
Answer$(3x - 1)(4x^3 - 2x^2 + 6x - 3)$
$= 3x (4x^3 - 2x^2 + 6x - 3) - 1 (4x^3 - 2x^2 + 6x - 3)$
$= 12x^4 - 6x^3 + 18x^2 - 9x - 4x^3 + 2x^2 - 6x + 3$
$= 12x^4 - 6x^3 - 4x^3 + 18x^2 + 2x^2 - 9x - 6x + 3$
$= 12x^4 - 10x^3 + 20x^2 - 15x + 3$
View full question & answer→Question 443 Marks
Copy and complete the following multi-plication:
$6 - 3x + 2x^2$
$\times 1 + 5x - x^2$
Answer$6 - 3x + 2x^2$
$\times 1 + 5x - x^2$
$6 - 3x + 2x^2$
$+ 30x - 15x^2 + 10x^3$
$- 6x^2 + 3x^3 - 2x^4$
$6 + 27x - 19x^2 + 13x^3 - 2x^4 $
View full question & answer→Question 453 Marks
Multiply: $6xy^2 - 7x^2y^2 + 10x^3$ and $- 3x^2y^3$
AnswerProduct of $6xy^2 - 7x^2y^2 + 10x^3$ and $- 3x^2y^3$
$= - 3x^2y^3 (6xy^2 - 7x^2y^2 + 10x^3)$
$= - 3x^2y^3 \times 6xy^2 + (- 3x^2y^3) \times (- 7x^2y^2 ) + (- 3x^2y^3) \times 10x^3$
$= - 18x^3y^5 + 21x^4y^5 - 30x^5y^3$
View full question & answer→Question 463 Marks
Multiply:$ - 3m^2n + 5mn - 4mn^2 and 6m^2n$
AnswerMultiply:$ - 3m^2n + 5mn - 4mn^2 and 6m^2n$
$= 6m^2n (- 3m^2n + 5mn - 4mn^2 )$
$= 6m^2n \times (- 3m^2n) + 6m^2n \times 5mn + 6m^2n \times (- 4mn^2)$
$= 18m^4n^2 + 30m^3n^2 - 24 m^3n^3$
View full question & answer→Question 473 Marks
Multiply: $9 x y+2 y^2$ and $2 x-3 y$
AnswerProduct of $9 x y+2 y^2$ and $2 x-3 y$
$=\left(9 x y+2 y^2\right) \times(2 x-3 y)$
$=18 x^2 y-23 x y^2-6 y^3$
$9 x y+2 y^2$
$\times 2 x-3 y$
$18 x^2 y+4 x y^2$
$-27 x y^2-6 y^2$
$18 x^2 y-23 x y^2-6 y^3$
View full question & answer→Question 483 Marks
The two adjacent sides of a rectangle are 6a + 96 and 8a- 46. Find its, perimeter.
AnswerSides of a rectangle are 6a + 9b
and 8a - 4b
Let, length = 6a + 9b
and breadth = 8a - 4b
∴ Perimeter = 2 (length + breadth)
= 2 (6a + 9b + 8a - 4b)
= 2 (14 a + 5 b)
= 28a + 10b
View full question & answer→Question 493 Marks
The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.
AnswerSides of a triangle are 2x + 3y, x + 5y, 7x - 2y
∴ Perimeter = sum of three sides of the triangle
= 2x + 3y + x + 5y + 7x - 2y
= 2x + x + 7x + 3y + 5y - 2y
= 10x + 8y - 2x
= 10x + 6y
View full question & answer→Question 503 Marks
Find the sum of: $4 x^3+2 x^2-x+1,2 x^3-5 x^2-3 x+6, x 2+8$ and $5 x^3-7 x$
Answer$4 x^3+2 x^2-x+1,2 x^3-5 x^2-3 x+6, x 2+8$ and $5 x^3-7 x$
$4 x^3+2 x^2-x+1+2 x^3-5 x^2-3 x+6+x^2+8+5 x^3-7 x$
$=4 x^3+2 x^3+5 x^3+2 x^2-5 x^2+x^2-x-3 x-7 x+1+6+8$
$=11 x^3+3 x^2-5 x^2-11 x+15$
$=11 x^3-2 x^2-11 x+15$
View full question & answer→