Question

Factorise 16(2a +b)² - 9(a -b)²​

Answer 1

Ok I will see the attached picture answer is (11a+b)(5a+7b)

Answer 2

$\sf\underline{\underline{ \large {Question :-}}}$

• Factorise 16(2a +b)² - 9(a -b)²

$\sf\underline{\underline{ \large {Answer :-}}}$

• (11 a + b)(5a + 7b)

$\sf\underline{\underline{ \large {Solution:-}}}$

$\sf\purple \mapsto{16 \: (2a \: + \: b)^2 \: - \: 9(a \: - \: b)^2}$

• Reducing it to squares for making the identity

$\sf\purple \mapsto{[4 \: (2a \: + \: b)]^2 \: - \: [3(a \: - \: b)]^2}$

$\sf{Using \: identity :}$

• $\sf\red{a^2 \: - \: b^2 \: = (a \: + \: b)(a \: - \: b)}$

$\sf\purple \mapsto{[4 \: (2a \: + \: b) \: + \: 3(a \: - \: b)][4(2a \: + \: b) \: - \: 3(a \: - \: b)]}$

$\sf\purple\mapsto{(8a \: + \: 4b \: + \: 3a \: - \: 3b)(8a \: + \: 4b \: - \: 3a \: + \: 3b)}$

$\sf\purple\mapsto\red{(11a \: + \: b)(5a \: + \: 7b)}$