Question

Factorise:
3a2b - 12a2-9b + 36​

Answer 1

3a

2

b−12a

2

−9b+36

Answer:

\begin{gathered}3 a ^ { 2 } b - 12 a ^ { 2 } - 9 b + 36 \\ \\ = 3a {}^{2} (b - 4) - 9(b - 4) \\ \\ = (b - 4)(3a {}^{2} - 9) \\ \\ = (b - 4)3(a {}^{2} - 3) \\ \\ = 3(b - 4)(a {}^{2} - 3) \\ \\ = 3(b - 4)(a - 3)(a + 3) \\ \\ (x {}^{2} - y {}^{2} = (x - y)(x + y)) \\ \\ hence. \: 3a {}^{2} b - 12a {}^{2} - 9b + 36 \\ = 3(b - 4)(a - 3)(a + 3)\end{gathered}

3a

2

b−12a

2

−9b+36

=3a

2

(b−4)−9(b−4)

=(b−4)(3a

2

−9)

=(b−4)3(a

2

−3)

=3(b−4)(a

2

−3)

=3(b−4)(a−3)(a+3)

(x

2

−y

2

=(x−y)(x+y))

hence.3a

2

b−12a

2

−9b+36

=3(b−4)(a−3)(a+3)

Answer 2

Answer:

$3 {a}^{2}b - 12 {a}^{2} - 9b + 36 \\ = 3 {a}^{2}(b - 4) - 9(b - 4) \\ = (3 {a}^{2} - 9)(b - 4) \\ 3( {a}^{2} - 3)(b - 4)$