Factorise :

${(a + b)}^{2} - 5 (a^{2} - b^{2}) - 24 {(a - b)}^{2}$

2 (2 a - b) (6 b + 5 a)

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2 (2 a - b) (6 b - 5 a)

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2 (2 a - b) (9 b - 7 a)

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2 (2 a - b) (9 b + 7 a)

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Solution

The correct option is C $2 (2 a - b) (9 b - 7 a)$
${(a + b)}^{2} - 5 (a^{2} - b^{2}) - 24 {(a - b)}^{2}$
$= {(a + b)}^{2} - 8 (a^{2} - b^{2}) + 3 (a^{2} - b^{2}) - 24 {(a - b)}^{2}$
$= {(a + b)}^{2} - 8 (a + b) (a - b) + 3 (a + b) (a - b) - 24 {(a - b)}^{2}$
$= (a + b) [(a + b) - 8 (a - b)] + 3 (a - b) [(a + b) - 8 (a - b)]$
$= (- 7 a + 9 b) (a + b + 3 (a - b))$
$= (- 7 a + 9 b) (4 a - 2 b)$
$= 2 (2 a - b) (9 b - 7 a)$

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