Question

Factorize (a + b)² – 5(a² – b²) – 24 (a - b)²​

Answer 1

GIVEN :-

• (a + b)² – 5(a² – b²) – 24 (a - b)²

SOLUTION :-

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

$\sf \: = (a + b) {}^{2} - 5(a + b)( a - b) - 24(a - b)$

$\sf \large \: Formula -$

• $\green{( {a}^{2} - {b}^{2} ) = (a + b)(a - b)}$

$\sf \: Let \: \: \pink{ A = (a+b) }\: \: and \: \: \pink{ B = ( a-b)}$

$\sf \: = {A}^{2} - 5.AB - 24B^{2}$

$\sf \: = {A}^{2} + 8A.B - 3A.B - 24B {}^{2}$

$\sf \: = A(A+ 8B )- 3B(A + 8B )$

$\sf \: = (A+ 8B )(A- 3B)$

$\sf \: Now \: \: replace \: \: A , \: and \: B$

$\sf \: = \{(a + b)+ 8(a - b) \} \{(a + b)- 3(a - b) \}$

$\sf \: = \{a + b+ 8a - 8b \} \{a + b- 3a + 3b) \}$

$\sf \: = (9a - 7b)(4b - 2a)$

Required Ans.......:)