Soalan 1:
Permudahkan setiap yang berikut. (a) \((3 x-2 y)+(5 x+9 y)\) (b) \((6 a b+2 b c+10)-(a b+3 b c-2)\) (c) \((4 x y+5 k)-(-3 k+7)+(13 x y-k)\) (d) \((7 p-8 q+6 p q)+(q-2 p+p q)-(10 p q-p-4 q)\) (e) \(\frac{2}{3} f g-\left(9 m n-\frac{1}{2} f g\right)+\left(3 m n-\frac{1}{6} f g\right)\)
Penyelesaian:
(a)
\[ \begin{aligned} & 3 x-2 y+(5 x+9 y) \\ & =3 x-2 y+5 x+9 y \\ & =(3 x+5 x)-2 y+9 y \\ & =8 x+7 y \end{aligned} \]
(b)
\[ \begin{aligned} & (6 a b+2 b c+10)-(a b+3 b c-2) \\ & =6 a b+2 b c+10-a b-3 b c+2 \\ & =6 a b-a b+2 b c-3 b c+10+2 \\ & =5 a b-b c+12 \end{aligned} \]
(c)
\[ \begin{aligned} & (4 x y+5 k)-(-3 k+7)+(13 x y-k) \\ & =4 x y+5 k+3 k-7+13 x y-k \\ & =4 x y+13 x y+5 k+3 k-k-7 \\ & =17 x y+7 k-7 \end{aligned} \]
(d)
\[ \begin{aligned} & (7 p-8 q+6 p q)+(q-2 p+p q)-(10 p q-p-4 q) \\ & =7 p-8 q+6 p q+q-2 p+p q-10 p q+p+4 q \\ & =7 p-2 p+p-8 q+q+4 q+6 p q+p q-10 p q \\ & =6 p-3 q-3 p q \end{aligned} \]
(e)
\begin{aligned} & \frac{2}{3} f g-\left(9 m n-\frac{1}{2} f g\right)+\left(3 m n-\frac{1}{6} f g\right) \\ & =\frac{2}{3} f g-9 m n+\frac{1}{2} f g+3 m n-\frac{1}{6} f g \\ & =\frac{2}{3} f g+\frac{1}{2} f g-\frac{1}{6} f g-9 m n+3 m n \\ & =\frac{4}{6} f g+\frac{3}{6} f g-\frac{1}{6} f g-6 m n \\ & =\frac{6}{6} f g-6 m n \\ & =f g-6 m n \end{aligned}
Permudahkan setiap yang berikut. (a) \((3 x-2 y)+(5 x+9 y)\) (b) \((6 a b+2 b c+10)-(a b+3 b c-2)\) (c) \((4 x y+5 k)-(-3 k+7)+(13 x y-k)\) (d) \((7 p-8 q+6 p q)+(q-2 p+p q)-(10 p q-p-4 q)\) (e) \(\frac{2}{3} f g-\left(9 m n-\frac{1}{2} f g\right)+\left(3 m n-\frac{1}{6} f g\right)\)
Penyelesaian:
(a)
\[ \begin{aligned} & 3 x-2 y+(5 x+9 y) \\ & =3 x-2 y+5 x+9 y \\ & =(3 x+5 x)-2 y+9 y \\ & =8 x+7 y \end{aligned} \]
(b)
\[ \begin{aligned} & (6 a b+2 b c+10)-(a b+3 b c-2) \\ & =6 a b+2 b c+10-a b-3 b c+2 \\ & =6 a b-a b+2 b c-3 b c+10+2 \\ & =5 a b-b c+12 \end{aligned} \]
(c)
\[ \begin{aligned} & (4 x y+5 k)-(-3 k+7)+(13 x y-k) \\ & =4 x y+5 k+3 k-7+13 x y-k \\ & =4 x y+13 x y+5 k+3 k-k-7 \\ & =17 x y+7 k-7 \end{aligned} \]
(d)
\[ \begin{aligned} & (7 p-8 q+6 p q)+(q-2 p+p q)-(10 p q-p-4 q) \\ & =7 p-8 q+6 p q+q-2 p+p q-10 p q+p+4 q \\ & =7 p-2 p+p-8 q+q+4 q+6 p q+p q-10 p q \\ & =6 p-3 q-3 p q \end{aligned} \]
(e)
\begin{aligned} & \frac{2}{3} f g-\left(9 m n-\frac{1}{2} f g\right)+\left(3 m n-\frac{1}{6} f g\right) \\ & =\frac{2}{3} f g-9 m n+\frac{1}{2} f g+3 m n-\frac{1}{6} f g \\ & =\frac{2}{3} f g+\frac{1}{2} f g-\frac{1}{6} f g-9 m n+3 m n \\ & =\frac{4}{6} f g+\frac{3}{6} f g-\frac{1}{6} f g-6 m n \\ & =\frac{6}{6} f g-6 m n \\ & =f g-6 m n \end{aligned}