Question

factorise 9(a-2b)^2-16(a-2b)^2

Answer 1

Given :


$\mathsf{9 \ {(a - 2b)}^{2} - 16 \ {(a - 2b)}^{2}}$


Taking common, we get


$\mathsf{= \ {(a - 2b)}^{2} \ [ \ 9 - 16 \ ]}$


$\mathsf{= \ {(a - 2b)}^{2} \ ( - 7)}$


{ Using identity –


$\bold{(a - b)^2 = a^2 + b ^2 - 2ab}$ }


$\mathsf{= \ ( - 7)({a}^{2} + 4 {b}^{2} - 4ab)}$


$\mathsf{= \ - 7 {a}^{2} - 14{b}^{2} + 28ab}$