Factorise using suitable identity:
${(6 a - 5 b)}^{2} - 9 {(a - 2 b)}^{2}$

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Solution

${(6 a - 5 b)}^{2} - 9 {(a - 2 b)}^{2}$
$= {(6 a - 5 b)}^{2} - {(3 a - 6 b)}^{2}$
$= (6 a - 5 b + 3 a - 6 b) (6 a - 5 b - (3 a - 6 b))$
$= (9 x - 11 b) (3 a + b)$

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