Soalan 1:
Permudah setiap yang berikut.
(a) 4(b − 1)2 − 9
(b) (m + 3)2 − 16
(c) (p − 5)2 − 49
(d) 7x(x − 1) − 3
(e) (2c − 1)2 + 2(4 + c)
Penyelesaian:
(a)
$$ \begin{aligned} 4(b-1)^2-9 & =2^2(b-1)^2-3 \\ & =[2(b-1)]^2-3^2 \\ & =[2(b-1)+3][2(b-1)-3] \\ & =(2 b-2+3)(2 b-2-3) \\ & =(2 b+1)(2 b-5) \end{aligned} $$
(b)
$$ \begin{aligned} (m+3)^2-16 & =(m+3)^2-4^2 \\ & =[m+3-4][m+3+4] \\ & =(m-1)(m+7) \end{aligned} $$
(c)
$$ \begin{aligned} (p-5)^2-49 & =(p-5)^2-7^2 \\ & =[p-5-7][p-5+7] \\ & =(p-12)(p+2) \end{aligned} $$
(d)
$$ 7 x(x-1)-3=7 x^2-7 x-3 $$
(e)
$$ \begin{aligned} (2 c-1)^2+2(4+c) & =(2 c-1)^2+8+2 c \\ & =(2 c-1)(2 c-1)+8+2 c \\ & =4 c^2-2 c-2 c+1+8+2 c \\ & =4 c^2-4 c+2 c+1+8 \\ & =4 c^2-2 c+9 \end{aligned} $$
Permudah setiap yang berikut.
(a) 4(b − 1)2 − 9
(b) (m + 3)2 − 16
(c) (p − 5)2 − 49
(d) 7x(x − 1) − 3
(e) (2c − 1)2 + 2(4 + c)
Penyelesaian:
(a)
$$ \begin{aligned} 4(b-1)^2-9 & =2^2(b-1)^2-3 \\ & =[2(b-1)]^2-3^2 \\ & =[2(b-1)+3][2(b-1)-3] \\ & =(2 b-2+3)(2 b-2-3) \\ & =(2 b+1)(2 b-5) \end{aligned} $$
(b)
$$ \begin{aligned} (m+3)^2-16 & =(m+3)^2-4^2 \\ & =[m+3-4][m+3+4] \\ & =(m-1)(m+7) \end{aligned} $$
(c)
$$ \begin{aligned} (p-5)^2-49 & =(p-5)^2-7^2 \\ & =[p-5-7][p-5+7] \\ & =(p-12)(p+2) \end{aligned} $$
(d)
$$ 7 x(x-1)-3=7 x^2-7 x-3 $$
(e)
$$ \begin{aligned} (2 c-1)^2+2(4+c) & =(2 c-1)^2+8+2 c \\ & =(2 c-1)(2 c-1)+8+2 c \\ & =4 c^2-2 c-2 c+1+8+2 c \\ & =4 c^2-4 c+2 c+1+8 \\ & =4 c^2-2 c+9 \end{aligned} $$
Soalan 2:
Permudah setiap yang berikut.
$$ \text { (a) } \frac{3 y}{5}+\frac{3 y}{5} $$
$$ \text { (b) } \frac{3 m+2 n}{m-2 n}-\frac{m-5 n}{m-2 n} $$
$$ \text { (c) } \frac{4 r-3 s}{2 r+3 s}-\frac{3 r-4 s}{2 r+3 s} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{3 y}{5}+\frac{3 y}{5} & =\frac{3 y+3 y}{5} \\ & =\frac{6 y}{5} \end{aligned} $$
(b)
$$ \begin{aligned} & \frac{3 m+2 n}{m-2 n}-\frac{m-5 n}{m-2 n} \\ & =\frac{3 m+2 n-(m-5 n)}{m-2 n} \\ & =\frac{3 m+2 n-m+5 n}{m-2 n} \\ & =\frac{3 m-m+2 n+5 n}{m-2 n} \\ & =\frac{2 m+7 n}{m-2 n} \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{4 r-3 s}{2 r+3 s}-\frac{3 r-4 s}{2 r+3 s} \\ & =\frac{4 r-3 s-(3 r-4 s)}{2 r+3 s} \\ & =\frac{4 r-3 s-3 r+4 s}{2 r+3 s} \\ & =\frac{4 r-3 r-3 s+4 s}{2 r+3 s} \\ & =\frac{r+s}{2 r+3 s} \end{aligned} $$
Permudah setiap yang berikut.
$$ \text { (a) } \frac{3 y}{5}+\frac{3 y}{5} $$
$$ \text { (b) } \frac{3 m+2 n}{m-2 n}-\frac{m-5 n}{m-2 n} $$
$$ \text { (c) } \frac{4 r-3 s}{2 r+3 s}-\frac{3 r-4 s}{2 r+3 s} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{3 y}{5}+\frac{3 y}{5} & =\frac{3 y+3 y}{5} \\ & =\frac{6 y}{5} \end{aligned} $$
(b)
$$ \begin{aligned} & \frac{3 m+2 n}{m-2 n}-\frac{m-5 n}{m-2 n} \\ & =\frac{3 m+2 n-(m-5 n)}{m-2 n} \\ & =\frac{3 m+2 n-m+5 n}{m-2 n} \\ & =\frac{3 m-m+2 n+5 n}{m-2 n} \\ & =\frac{2 m+7 n}{m-2 n} \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{4 r-3 s}{2 r+3 s}-\frac{3 r-4 s}{2 r+3 s} \\ & =\frac{4 r-3 s-(3 r-4 s)}{2 r+3 s} \\ & =\frac{4 r-3 s-3 r+4 s}{2 r+3 s} \\ & =\frac{4 r-3 r-3 s+4 s}{2 r+3 s} \\ & =\frac{r+s}{2 r+3 s} \end{aligned} $$
Soalan 3:
Permudah setiap yang berikut.
$$ \text { (a) } \frac{5}{p}-\frac{2}{p^2} $$
$$ \text { (b) } \frac{2 s}{3}-\frac{4 s}{9} $$
$$ \text { (c) } \frac{3}{x+y}-\frac{3 z}{4(x+y)} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{5}{p}-\frac{2}{p^2} & =\frac{5 \times p}{p \times p}-\frac{2}{p^2} \\ & =\frac{5 p-2}{p^2} \end{aligned} $$
(b)
$$ \begin{aligned} \frac{2 s}{3}-\frac{4 s}{9} & =\frac{2 s \times 3}{3 \times 3}-\frac{4 s}{9} \\ & =\frac{6 s-4 s}{9} \\ & =\frac{2 s}{9} \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{3}{x+y}-\frac{3 z}{4(x+y)} \\ = & \frac{3 \times 4}{4 \times(x+y)}-\frac{3 z}{4(x+y)} \\ = & \frac{12}{4(x+y)}-\frac{3 z}{4(x+y)} \\ = & \frac{12-3 z}{4(x+y)} \end{aligned} $$
Permudah setiap yang berikut.
$$ \text { (a) } \frac{5}{p}-\frac{2}{p^2} $$
$$ \text { (b) } \frac{2 s}{3}-\frac{4 s}{9} $$
$$ \text { (c) } \frac{3}{x+y}-\frac{3 z}{4(x+y)} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{5}{p}-\frac{2}{p^2} & =\frac{5 \times p}{p \times p}-\frac{2}{p^2} \\ & =\frac{5 p-2}{p^2} \end{aligned} $$
(b)
$$ \begin{aligned} \frac{2 s}{3}-\frac{4 s}{9} & =\frac{2 s \times 3}{3 \times 3}-\frac{4 s}{9} \\ & =\frac{6 s-4 s}{9} \\ & =\frac{2 s}{9} \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{3}{x+y}-\frac{3 z}{4(x+y)} \\ = & \frac{3 \times 4}{4 \times(x+y)}-\frac{3 z}{4(x+y)} \\ = & \frac{12}{4(x+y)}-\frac{3 z}{4(x+y)} \\ = & \frac{12-3 z}{4(x+y)} \end{aligned} $$
Soalan 4:
Permudah setiap yang berikut.
$$ \text { (a) } \frac{3 u}{4}+\frac{5 v}{3} $$
$$ \text { (b) } \frac{1}{6 s}-\frac{2}{5 t} $$
$$ \text { (c) } \frac{2}{r-2}+\frac{4}{3 s} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{3 u}{4}+\frac{5 v}{3} & =\frac{3 u \times 3}{4 \times 3}+\frac{5 v \times 4}{3 \times 4} \\ & =\frac{9 u}{12}+\frac{20 v}{12} \\ & =\frac{9 u+20 v}{12} \end{aligned} $$
(b)
$$ \begin{aligned} \frac{1}{6 s}-\frac{2}{5 t} & =\frac{1 \times 5 t}{6 s \times 5 t}-\frac{2 \times 6 s}{5 t \times 6 s} \\ & =\frac{5 t}{30 s t}-\frac{12 s}{30 s t} \\ & =\frac{5 t-12 s}{30 s t} \end{aligned} $$
(c)
$$ \begin{aligned} \frac{2}{r-2}+\frac{4}{3 s} & =\frac{2 \times 3 s}{(r-2) \times 3 s}+\frac{4 \times(r-2)}{3 s \times(r-2)} \\ & =\frac{6 s}{3 s(r-2)}+\frac{4(r-2)}{3 s(r-2)} \\ & =\frac{6 s+4(r-2)}{3 s(r-2)} \\ & =\frac{6 s+4 r-8}{3 s(r-2)} \\ & =\frac{6 s+4 r-8}{3 r s-6} \end{aligned} $$
Permudah setiap yang berikut.
$$ \text { (a) } \frac{3 u}{4}+\frac{5 v}{3} $$
$$ \text { (b) } \frac{1}{6 s}-\frac{2}{5 t} $$
$$ \text { (c) } \frac{2}{r-2}+\frac{4}{3 s} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{3 u}{4}+\frac{5 v}{3} & =\frac{3 u \times 3}{4 \times 3}+\frac{5 v \times 4}{3 \times 4} \\ & =\frac{9 u}{12}+\frac{20 v}{12} \\ & =\frac{9 u+20 v}{12} \end{aligned} $$
(b)
$$ \begin{aligned} \frac{1}{6 s}-\frac{2}{5 t} & =\frac{1 \times 5 t}{6 s \times 5 t}-\frac{2 \times 6 s}{5 t \times 6 s} \\ & =\frac{5 t}{30 s t}-\frac{12 s}{30 s t} \\ & =\frac{5 t-12 s}{30 s t} \end{aligned} $$
(c)
$$ \begin{aligned} \frac{2}{r-2}+\frac{4}{3 s} & =\frac{2 \times 3 s}{(r-2) \times 3 s}+\frac{4 \times(r-2)}{3 s \times(r-2)} \\ & =\frac{6 s}{3 s(r-2)}+\frac{4(r-2)}{3 s(r-2)} \\ & =\frac{6 s+4(r-2)}{3 s(r-2)} \\ & =\frac{6 s+4 r-8}{3 s(r-2)} \\ & =\frac{6 s+4 r-8}{3 r s-6} \end{aligned} $$