Question 12 Marks
Simplify: 6a – (- 5a – 8b) + (3a + b)
Answer6a – (- 5a – 8b) + (3a + b)
= 6a + 5a + 8b + 3a + b
= 6a + 5a + 3a + 8b + b
= 14a + 9b
View full question & answer→Question 22 Marks
Simplify $: (x + y – z)x + (z + x – y)y – (x + y – z)z$
Answer$(x + y – z)x + (z + x – y)y – (x + y – z)z$
$= x^2+ xy – zx + yz + xy -y^2 – zx – yz + z^2$
$= x^2 - y^2 + z^2 + 2xy – 2zx$
View full question & answer→Question 32 Marks
Simplify: {9 – (4p – 6q)} – {3q – (5p – 10)}
Answer{9 – (4p – 6q)} – {3q – (5p – 10)}
= {9 – 4p + 6q} – {3q -5p+ 10}
= 9 – 4p + 6q – 3q + 5p – 10
= 9 – 4p + 5p + 6q – 3q – 10
= p + 3q – 1
View full question & answer→Question 42 Marks
Simplify: 8 [m + 2n-p – 7 (2m -n + 3p)]
Answer8 [m + 2n - p – 7 (2m - n + 3p)]
= 8 [m + 2n - p- 14m + 7n - 21p]
= 8m+ 16n - 8p - 112m + 56n – 168p
= 8m – 112m + 16n + 56n - 8p – 168p
= -104m + 72n – 176p
View full question & answer→Question 52 Marks
Simplify: 5b – {6a + (8 – b – a)}
Answer5b – {6a + (8 – b – a)}
= 5b – 6a – 8 + b + a
= -6a + a + 5b +b – 8
= -5a + 6b - 8
View full question & answer→Question 62 Marks
Simplify: $2 \mathrm{a}+(6-\overline{\mathrm{a}-\mathrm{b}})$
Answer$\begin{aligned} & 2 a+(6-\overline{a-b}) \\ & =2 a+(b-a+b) \\ & =2 a+b-a+b \\ & =a+2 b\end{aligned}$
View full question & answer→Question 72 Marks
Answer5 - 8x - 6 - x
= 5 - 6 - 8x - x
= -1 - 9x
View full question & answer→Question 82 Marks
Simplify: a + (b + c – d)
Answera + (b + c – d)
= a + (b + c – d)
= a + b + c – d
View full question & answer→Question 92 Marks
Simplify: $5 x (2x + 3y) – 2x (x – 9y)$
Answer$5 x (2x + 3y) – 2x (x – 9y)$
$= 10x^2 + 15xy – 2x^2 + 18xy$
$= 10x^2 – 2x^2 + 15xy+ 18xy$
$= 8x^2 + 33xy$
View full question & answer→Question 102 Marks
Simplify: $\mathrm{a}\left(\mathrm{a}+\frac{1}{\mathrm{a}}\right)-\mathrm{b}\left(\mathrm{b}-\frac{1}{\mathrm{~b}}\right)-\mathrm{c}\left(\mathrm{c}+\frac{1}{\mathrm{c}}\right)$
Answer
$\begin{aligned} & a\left(a+\frac{1}{a}\right)-b\left(b-\frac{1}{b}\right)-c\left(c+\frac{1}{c}\right) \\ & =a^2+1-b^2+1-c^2-1 \\ & =a^2-b^2-c^2+1\end{aligned}$
View full question & answer→Question 112 Marks
Simplify: 8 (2a + 3b – c) – 10 (a + 2b + 3c)
Answer8 (2a + 3b – c) – 10 (a + 2b + 3c)
= 16a + 24b – 8c – 10a – 20b- 30c
= 16a – 10a + 24b – 20b – 8c – 30c
= 6a + 4b – 38c
View full question & answer→Question 122 Marks
Simplify: $- 2x (x + y) + x^2$
Answer$- 2x (x + y) + x^2$
$= -2x \times x + (-2x)y + x^2$
$= – 2x^2 – 2xy + x^2$
$= – 2x^2 + x^2 – 2xy = – x^2 – 2xy$
View full question & answer→Question 132 Marks
Simplify $: -5m (-2m + 3n – 7p)$
Answer$- 5m (-2m + 3n – 7p)$
$= – 5m x (-2m) + (-5m) (3n) – (-5m) (7p)$
$= 10m^2 – 15mn + 35 mp.$
View full question & answer→Question 142 Marks
Simplify: $\frac{4 a}{7}+\frac{2 a}{3}-\frac{a}{7}$
Answer
$\begin{aligned} & \frac{4 \mathrm{a}}{7}+\frac{2 \mathrm{a}}{3}-\frac{\mathrm{a}}{7} \\ & =\frac{12 \mathrm{a}-14 \mathrm{a}+3 \mathrm{a}}{21} \\ & =\frac{15 \mathrm{a}-14 \mathrm{a}}{21} \\ & =\frac{\mathrm{a}}{21} \ldots(\text { LCM of } 7,3=21)\end{aligned}$
View full question & answer→Question 152 Marks
Simplify: $\frac{7}{30}$ of $\left(\frac{\mathrm{p}}{3}+\frac{7 \mathrm{p}}{15}\right)$
Answer
$\begin{aligned} & \frac{7}{30} \text { of }\left(\frac{\mathrm{p}}{3}+\frac{7 \mathrm{p}}{15}\right) \\ & =\frac{7}{3} \text { of }\left(\frac{5 \mathrm{p}+7 \mathrm{p}}{15}\right) \\ & =\frac{7}{30} \times \frac{12}{15} \mathrm{p} \\ & =\frac{14 \mathrm{p}}{75}\end{aligned}$
View full question & answer→Question 162 Marks
Simplify: $\frac{m}{5}-\frac{m-2}{3}+m$
Answer
$\begin{aligned} & \frac{\mathrm{m}}{5}-\frac{\mathrm{m}-2}{3}+\frac{\mathrm{m}}{1} \\ & =\frac{3 \mathrm{~m}-5(\mathrm{~m}-2)+15 \mathrm{~m}}{15} \\ & =\frac{3 \mathrm{~m}-5 \mathrm{~m}+10+15 \mathrm{~m}}{15} \\ & =\frac{18 \mathrm{~m}-5 \mathrm{~m}+10}{15} \\ & =\frac{13 \mathrm{~m}+10}{15}\end{aligned}$
View full question & answer→Question 172 Marks
Simplify: $\frac{\mathrm{k}+1}{2}+\frac{2 \mathrm{k}-1}{3}-\frac{\mathrm{k}+3}{4}$
Answer
$\begin{aligned} & \frac{\mathrm{k}+1}{2}+\frac{2 \mathrm{k}-1}{3}-\frac{\mathrm{k}+3}{4} \\ & =\frac{6 \mathrm{k}+6+8 \mathrm{k}-4-3 \mathrm{k}-9}{12} \ldots(\mathrm{LCM} \text { of } 2,3,4=12) \\ & =\frac{14 \mathrm{k}-3 \mathrm{k}+6-13}{12} \\ & =\frac{11 \mathrm{k}-7}{12}\end{aligned}$
View full question & answer→Question 182 Marks
Simplify: $\frac{3 y}{5}-\frac{y+2}{2}$
Answer
$\begin{aligned} & \frac{3 y}{5}-\frac{y+2}{2} \\ & =\frac{6 y-(5 y+10)}{10} \\ & =\frac{6 y-5 y-10}{10} \\ & =\frac{y-10}{10}\end{aligned}$
View full question & answer→Question 192 Marks
Simplify: $\mathrm{x}+\frac{\mathrm{x}+2}{3}$
Answer
$\begin{aligned} & x+\frac{x+2}{3} \\ & =\frac{x}{1}+\frac{x+2}{3} \\ & =\frac{3 x+x+2}{3}=\frac{4 x+2}{3}\end{aligned}$
View full question & answer→Question 202 Marks
Simplify: $\mathrm{x}+\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}$
Answer
$\begin{aligned} & x+\frac{x}{2}+\frac{x}{3} \\ & =\frac{x}{1}+\frac{x}{2}+\frac{x}{3} \\ & =\frac{6 x+3 x+2 x}{6}=\frac{11 x}{6}\end{aligned}$
View full question & answer→Question 212 Marks
Simplify: $\frac{3 \mathrm{a}}{8}+\frac{4 \mathrm{a}}{5}-\left(\frac{\mathrm{a}}{2}+\frac{2 \mathrm{a}}{5}\right)$
Answer
$\begin{aligned} & \frac{3 a}{8}+\frac{4 a}{5}-\left(\frac{a}{2}+\frac{2 a}{5}\right) \\ & =\frac{15 a+32 a-(20 a+16 a)}{40} \ldots(\text { LCM of } 8,5,2=40) \\ & =\frac{47 a-36 a}{40}=\frac{11 a}{40}\end{aligned}$
View full question & answer→Question 222 Marks
Simplify: $\frac{6 \mathrm{k}}{7}-\left(\frac{8 \mathrm{k}}{9}-\frac{\mathrm{k}}{3}\right)$
Answer
$\begin{aligned} & \frac{6 \mathrm{k}}{7}-\left(\frac{8 \mathrm{k}}{9}-\frac{\mathrm{k}}{3}\right) \\ & =\frac{54 \mathrm{k}-(56 \mathrm{k}-21 \mathrm{k})}{63} \quad \ldots(\mathrm{LCM} \text { of } 7,9,3=63) \\ & =\frac{54 \mathrm{k}-(35 \mathrm{k})}{63} \\ & =\frac{54 \mathrm{k}-35 \mathrm{k}}{63}=\frac{19 \mathrm{k}}{63}\end{aligned}$
View full question & answer→Question 232 Marks
Simplify: $\frac{2 b}{5}-\frac{7 b}{15}+\frac{13 b}{3}$
Answer
$\begin{aligned} & \frac{2 \mathrm{~b}}{5}-\frac{7 \mathrm{~b}}{15}+\frac{13 \mathrm{~b}}{3} \ldots(\mathrm{LCM} \text { of } 3,5,15=15) \\ & =\frac{6 \mathrm{~b}-7 \mathrm{~b}+65 \mathrm{~b}}{15} \\ & =\frac{71 \mathrm{~b}-7 \mathrm{~b}}{15} \\ & =\frac{64 \mathrm{~b}}{15}\end{aligned}$
View full question & answer→Question 242 Marks
Simplify: $\frac{x}{2}+\frac{x}{4}$
Answer
$\begin{aligned} & \frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{4} \\ & =\frac{2 \mathrm{x}+\mathrm{x}}{4}=\frac{3 \mathrm{x}}{4}\end{aligned}$
View full question & answer→Question 252 Marks
Divide $: x^5 - 15x^4 - 10x^2 by -5x^2$
Answer
$\begin{aligned} & x^5-15 x^4-10 x^2 \text { by }-5 x^2 \\ & =\frac{x^5-15 x^4-10 x^2}{-5 x^2} \\ & =\frac{x^5}{-5 x^2}-\frac{15 x^4}{-5 x^2}-\frac{10 x^2}{-5 x^2} \\ & =\frac{-1}{5} x^3+3 x^2+2\end{aligned}$
View full question & answer→Question 262 Marks
Divide: $3y^3 - 9ay^2 - 6ab^2y$ by $-3y$
Answer
$\begin{aligned} & 3 y^3-9 a y^2-6 a b^2 y \text { by -3y } \\ & =\frac{3 y^3-9 a y^2-6 a b y^2}{-3 y} \\ & =\frac{3 y^3}{-3 y}-\frac{9 a y^3}{-3 y}-\frac{-6 a b^2 y}{-3 y} \\ & =-y^2+3 a y^2+2 a b^2\end{aligned}$
View full question & answer→Question 272 Marks
Divide: $10x^3y - 9xy^2 - 4x^2y^2$^ by $xy$
Answer
$\begin{aligned} & 10 x^3 y-9 x y^2-4 x^2 y^2 \text { by } x y \\ & =\frac{10 x^3 y-9 x y^2-4 x^2 y^2}{x y} \\ & =\frac{10 x^3 y}{x y}-\frac{9 x y^2}{x y}-\frac{4 x^2 y^2}{x y} \\ & =10 x^2-9 y-4 x y\end{aligned}$
View full question & answer→Question 282 Marks
Divide: $5x^2 - 3x$ by $x$
Answer
$\begin{aligned} & 5 x^2-3 x \text { by } x \\ & =\frac{5 x^2-3 x}{x}=\frac{5 x^2}{x}-\frac{3 x}{x} \\ & =5 x-3\end{aligned}$
View full question & answer→Question 292 Marks
Divide: $2m^3n^5$ by $- mn$
Answer$2 m^3 n^5$ by $-m n$
$=\frac{2 m^3 n^5}{-m n}$
$=-2 m^2 n^4$
View full question & answer→Question 302 Marks
Divide: $4x^3 - 2x^2 by - x$
Answer
$\begin{aligned} & 4 x^3-2 x^2 \text { by -x } \\ & =\frac{4 x^3-2 x^2}{-x}=\frac{4 x^3}{-x}-\frac{2 x^2}{-x} \\ & =-4 x^2+2 x\end{aligned}$
View full question & answer→Question 312 Marks
Divide: - 50 + 40p by 10p
Answer
$\begin{aligned} & -50+40 p \text { by } 10 p \\ & =\frac{-50+40 p}{10 p}=\frac{-50}{10 p}+\frac{40 p}{10 p} \\ & =-\frac{5}{p}+4\end{aligned}$
View full question & answer→Question 322 Marks
Answer
$\begin{aligned} & 8 m-16 \text { by }-8 \\ & =\frac{8 m-16}{-8}=\frac{8 m}{-8}=\frac{16}{-8}=-m+2\end{aligned}$
View full question & answer→Question 332 Marks
Divide: $4a^2 - a by - a$
Answer
$\begin{aligned} & 4 a^2-a b y-a \\ & =\frac{4 a^2-a}{-a}=\frac{4 a^2}{-a}-\frac{a}{-a} \\ & =-4 a+1\end{aligned}$
View full question & answer→Question 342 Marks
Answer
$\begin{aligned} & 8 x+24 \text { by } 4 \\ & =\frac{8 x+24}{4}=\frac{8 x}{4}+\frac{24}{4} \\ & =2 x+6\end{aligned}$
View full question & answer→Question 352 Marks
Divide: $25x^2y$ by $- 5y^2$
Answer
$\begin{aligned} & 25 x^2 y \text { by }-5 y^2 \\ & =\frac{25 x^2 y}{-} 5 y^2 \\ & =-5 \frac{x^2}{y}\end{aligned}$
View full question & answer→Question 362 Marks
Divide: $- 16ab^2c$ by $6abc$
Answer$-16 a b^2 c$ by $6 a b c$
$ \begin{aligned} & =\frac{-16 a b^2 c}{6 a b c} \\ & =-\frac{8}{3} b \end{aligned} $
View full question & answer→Question 372 Marks
Multiply: $(6x - 2y)(3x - y)$
Answer$(6x - 2y)(3x - y)$
$\Rightarrow 6x (3x - y) - 2y (3x - y)$
$\Rightarrow 18x^2 - 6xy - 6xy + 2y^2$
$\Rightarrow 18x^2 - 12xy + 2y^2$
View full question & answer→Question 382 Marks
Multiply: $(x - a)(x + 3b)$
Answer$(x - a)(x + 3b)$
$\Rightarrow x (x + 3b) - a (x + 3b)$
$\Rightarrow x^2 + 3bx - ax - 3ab$
View full question & answer→Question 392 Marks
Multiply:$ (xy + 2b)(xy - 2b)$
Answer$(xy + 2b)(xy - 2b)$
$\Rightarrow xy (xy - 2b) + 2b (xy - 2b)$
$\Rightarrow x^2y^2 - 2bxy + 2bxy - 4b^2$
$\Rightarrow x^2y^2 - 4b^2$
View full question & answer→Question 402 Marks
Multiply: $(-2x + 3y)(2x - 3y)$
Answer$(- 2x + 3y)(2x - 3y)$
$\Rightarrow - 2x (2x - 3y) + 3y(2x - 3y)$
$\Rightarrow - 4x^2 + 6xy + 6xy - 9y^2$
$\Rightarrow - 4x^2 + 12xy - 9y^2$
View full question & answer→Question 412 Marks
Multiply: $(2x + 3y)(2x + 3y)$
Answer$(2x + 3y)(2x + 3y)$
$\Rightarrow 2x (2x + 3y) + 3y(2x + 3y)$
$\Rightarrow 4x^2 + 6xy + 6xy + 9y^2$
$\Rightarrow 4x^2 + 12xy + 9y^2$
View full question & answer→Question 422 Marks
Multiply: $x^2 + 5yx - 3y^2$^ and $2x^2y$
Answer$x^2 + 5yx - 3y^2$ and $2x^2y$
$\Rightarrow 2x^2y \times (x^2 + 5yx - 3y^2)$
$\Rightarrow 2x^4y + 10x^3y^2 - 6x^2y^3$
View full question & answer→Question 432 Marks
Multiply: $a^3 - 4ab$ and $2a^2b$
Answer$a^3 - 4ab$ and $2a^2b$
$\Rightarrow 2a^2b \times (a^3 - 4ab)$
$\Rightarrow 2a^5b - 8a^3b^2$
View full question & answer→Question 442 Marks
Multiply: $x^3 - 3y^3$ and $4x^2y^2$
Answer$x^3 - 3y^3$ and $4x^2y^2$
$\Rightarrow 4x^2y^2 \times (x^3 - 3y^3)$
$\Rightarrow 4x^5y^2 - 12x^2y^5$
View full question & answer→Question 452 Marks
Multiply: $pq - pm$ and $p^2m$
Answer$pq - pm$ and $p^2m$
$\Rightarrow p^2m \times (pq - pm)$
$\Rightarrow p^3qm - p^3m^2$
View full question & answer→Question 462 Marks
Multiply: 2mnpq, 4mnpq and 5 mnpq
Answer$2 \mathrm{mnpq}, 4 \mathrm{mnpq}$ and $5 \mathrm{mnpq}$
$ \begin{aligned} & \Rightarrow 5 \mathrm{mnpq} \times 2 \mathrm{mnpq} \times 4 \mathrm{mnpq} \\ & \Rightarrow 5 \times 2 \times 4 \mathrm{~m}^{1+1+1} \mathrm{n}^{1+1+1} \mathrm{p}^{1+1+1} \mathrm{q}^{1+1+1} \\ & \Rightarrow 40 \mathrm{~m}^3 \mathrm{n}^3 \mathrm{p}^3 \mathrm{q}^3 \end{aligned} $
View full question & answer→Question 472 Marks
Multiply: $mn^4, m^3n$ and $5m^2n^3$
Answer
$\begin{aligned} & \mathrm{mn}^4, \mathrm{~m}^3 \mathrm{n} \text { and } 5 \mathrm{~m}^2 \mathrm{n}^3 \\ & \Rightarrow 5 \mathrm{~m}^2 \mathrm{n}^3 \times \mathrm{mn}^4 \times \mathrm{m}^3 \mathrm{n} \\ & \Rightarrow 5 \mathrm{~m}^{2+1+3} \mathrm{n}^{3+4+1} \\ & =5 \mathrm{~m}^6 \mathrm{n}^8\end{aligned}$
View full question & answer→Question 482 Marks
Evaluate: $(6p^2 - 8pq + 2q^2) (- 5p)$
Answer$(6p^2 - 8pq + 2q^2) (- 5p)$
$= -5p \times 6p^2 - 5p \times (- 8pq) - 5p (2q^2)$
$= - 30p^3 + 40p^2q - 10pq^2$
View full question & answer→Question 492 Marks
Evaluate: $(a^2 + 2ab + b^2)(a + b)$
Answer$(a^2 + 2ab + b^2)(a + b)$
$= a(a^2 + 2ab + b^2) + b(a^2 + 2ab + b^2)$
$= a^3 + 2a^2b + ab^2 + a^2b + 2ab^2 + b^3$
$= a^3 + 3a^2b + 3ab^2 + b^3$
View full question & answer→Question 502 Marks
Evaluate: $\left(\frac{1}{2} a+\frac{1}{2} b\right)\left(\frac{1}{2} a-\frac{1}{2} b\right)$
Answer
$\begin{aligned} & \left(\frac{1}{2} a+\frac{1}{2} b\right)\left(\frac{1}{2} a-\frac{1}{2} b\right) \\ & =\frac{1}{2 a}\left(\frac{1}{2} a-\frac{1}{2} b\right)+\frac{1}{2} b\left(\frac{1}{2} a-\frac{1}{2} b\right) \\ & =\frac{1}{4} a^2-\frac{1}{4} a b+\frac{1}{4} a b-\frac{1}{4} b^2 \\ & =\frac{1}{4} a^2-\frac{1}{4} b^2\end{aligned}$
View full question & answer→