Soalan 1:
Kembangkan setiap ungkapan berikut.
$$ \text { (a) } \frac{1}{2}(6 a+12 b) $$
$$ \text { (b) }(n+2)(n-5) $$
$$ \text { (c) }(a+2 b)^2 $$
$$ \text { (d) }(4 x-y)^2 $$
$$ \text { (e) }\left(2 v-\frac{1}{3 w}\right)\left(3 v+\frac{2}{3 w}\right) $$
$$ \text { (f) }(h-k)^2-4 h(2 k-3 h) $$
Penyelesaian:
(a)
(b)
(c)
$$ \begin{aligned} & (a+2 b)^2 \\ & =(a+2 b)(a+2 b) \\ & =a^2+2 a b+2 a b+4 b^2 \\ & =a^2+4 a b+4 b^2 \end{aligned} $$
(d)
$$ \begin{aligned} & (4 x-y)^2 \\ & =(4 x-y)(4 x-y) \\ & =16 x^2-4 x y-4 x y+y^2 \\ & =16 x^2-8 x y+y^2 \end{aligned} $$
(e)
$$ \begin{aligned} \left(2 v-\frac{1}{3 w}\right)\left(3 v+\frac{2}{3 w}\right) & =6 v^2+\frac{4 v}{3 w}-\frac{3 v}{3 w}-\frac{2}{9 w^2} \\ & =6 v^2+\left(\frac{4 v-3 v}{3 w}\right)-\frac{2}{9 w^2} \\ & =6 v^2+\frac{v}{3 w}-\frac{2}{9 w^2} \end{aligned} $$
(f)
$$ \begin{aligned} (h-k)^2-4 h(2 k-3 h) & =(h-k)(h-k)-8 h k+12 h^2 \\ & =h^2-h k-h k+k^2-8 h k+12 h^2 \\ & =13 h^2-10 h k+k^2 \end{aligned} $$
Kembangkan setiap ungkapan berikut.
$$ \text { (a) } \frac{1}{2}(6 a+12 b) $$
$$ \text { (b) }(n+2)(n-5) $$
$$ \text { (c) }(a+2 b)^2 $$
$$ \text { (d) }(4 x-y)^2 $$
$$ \text { (e) }\left(2 v-\frac{1}{3 w}\right)\left(3 v+\frac{2}{3 w}\right) $$
$$ \text { (f) }(h-k)^2-4 h(2 k-3 h) $$
Penyelesaian:
(a)
(b)
(c)
$$ \begin{aligned} & (a+2 b)^2 \\ & =(a+2 b)(a+2 b) \\ & =a^2+2 a b+2 a b+4 b^2 \\ & =a^2+4 a b+4 b^2 \end{aligned} $$
(d)
$$ \begin{aligned} & (4 x-y)^2 \\ & =(4 x-y)(4 x-y) \\ & =16 x^2-4 x y-4 x y+y^2 \\ & =16 x^2-8 x y+y^2 \end{aligned} $$
(e)
$$ \begin{aligned} \left(2 v-\frac{1}{3 w}\right)\left(3 v+\frac{2}{3 w}\right) & =6 v^2+\frac{4 v}{3 w}-\frac{3 v}{3 w}-\frac{2}{9 w^2} \\ & =6 v^2+\left(\frac{4 v-3 v}{3 w}\right)-\frac{2}{9 w^2} \\ & =6 v^2+\frac{v}{3 w}-\frac{2}{9 w^2} \end{aligned} $$
(f)
$$ \begin{aligned} (h-k)^2-4 h(2 k-3 h) & =(h-k)(h-k)-8 h k+12 h^2 \\ & =h^2-h k-h k+k^2-8 h k+12 h^2 \\ & =13 h^2-10 h k+k^2 \end{aligned} $$
Soalan 2:
Faktorkan setiap ungkapan berikut.
(a) 12m – 18m2
(b) y2 – 81
(c) 4ab – 8a2 b
(d) x2 – 16y2
(e) (s – 3)2 – 1
(f) x2 + 4x + 3
(g) x2 + 2x – 15
(h) x2 + 6x + 8
(i) 6cd – 2ce – 3bd + be
Penyelesaian:
(a)
$$ \begin{aligned} &12 m-18 m^2\\ &\text { Faktor sepunya }\\ &\begin{aligned} & =6 \operatorname{dan} m \\ & =6 m(2-3 m) \end{aligned} \end{aligned} $$
(b)
$$ \begin{aligned} & y^2-81 \\ & =y^2-9^2 \\ & =(y+9)(y-9) \end{aligned} $$
(c)
$$ \begin{aligned} &4 a b-8 a^2 b\\ &\text { Faktor sepunya }\\ &\begin{aligned} & =4, a \operatorname{dan} b \\ & =4 a b(1-2 a) \end{aligned} \end{aligned} $$
(d)
$$ \begin{aligned} & x^2-16 y^2 \\ & =x^2-(4 y)^2 \\ & =(x+4 y)(x-4 y) \end{aligned} $$
(e)
$$ \begin{aligned} & (s-3)^2-1 \\ & =(s-3)^2-1^2 \\ & =[(s-3)+1][(s-3)-1] \\ & =(s-3+1)(s-3-1) \\ & =(s-2)(s-4) \end{aligned} $$
(f)
$$ \begin{aligned} & x^2+4 x+3 \\ & =(x+3)(x+1) \end{aligned} $$
(g)
$$ \begin{aligned} & x^2+2 x-15 \\ & =(x+5)(x-3) \end{aligned} $$
(h)
$$ \begin{aligned} & x^2+6 x+8 \\ & =(x+2)(x+4) \end{aligned} $$
(i)
$$ \begin{aligned} & 6 c d-2 c e-3 b d+b e \\ & =2 c(3 d-e)-b(3 d-e) \\ & =(2 c-b)(3 d-e) \end{aligned} $$
Faktorkan setiap ungkapan berikut.
(a) 12m – 18m2
(b) y2 – 81
(c) 4ab – 8a2 b
(d) x2 – 16y2
(e) (s – 3)2 – 1
(f) x2 + 4x + 3
(g) x2 + 2x – 15
(h) x2 + 6x + 8
(i) 6cd – 2ce – 3bd + be
Penyelesaian:
(a)
$$ \begin{aligned} &12 m-18 m^2\\ &\text { Faktor sepunya }\\ &\begin{aligned} & =6 \operatorname{dan} m \\ & =6 m(2-3 m) \end{aligned} \end{aligned} $$
(b)
$$ \begin{aligned} & y^2-81 \\ & =y^2-9^2 \\ & =(y+9)(y-9) \end{aligned} $$
(c)
$$ \begin{aligned} &4 a b-8 a^2 b\\ &\text { Faktor sepunya }\\ &\begin{aligned} & =4, a \operatorname{dan} b \\ & =4 a b(1-2 a) \end{aligned} \end{aligned} $$
(d)
$$ \begin{aligned} & x^2-16 y^2 \\ & =x^2-(4 y)^2 \\ & =(x+4 y)(x-4 y) \end{aligned} $$
(e)
$$ \begin{aligned} & (s-3)^2-1 \\ & =(s-3)^2-1^2 \\ & =[(s-3)+1][(s-3)-1] \\ & =(s-3+1)(s-3-1) \\ & =(s-2)(s-4) \end{aligned} $$
(f)
$$ \begin{aligned} & x^2+4 x+3 \\ & =(x+3)(x+1) \end{aligned} $$
(g)
$$ \begin{aligned} & x^2+2 x-15 \\ & =(x+5)(x-3) \end{aligned} $$
(h)
$$ \begin{aligned} & x^2+6 x+8 \\ & =(x+2)(x+4) \end{aligned} $$
(i)
$$ \begin{aligned} & 6 c d-2 c e-3 b d+b e \\ & =2 c(3 d-e)-b(3 d-e) \\ & =(2 c-b)(3 d-e) \end{aligned} $$