Question

Factorize using algebraic identity 4 (x+1)^2-49

Answer 1

$hi...$
To factorize the above question
we may use identity of :
${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$
So ..

$4 ({x + 1)}^{2} - 49$

$= 4( {x}^{2} + 2x + 1) - 49$

$= 4 {x}^{2} + 8x + 4 - 49$

$= 4 {x}^{2} + 8x - 45$

$= 4x ^{2} + 18x - 10x - 45$

$= 2x(2x + 9) - 5(2x + 9)$

$= (2x + 9)(2x - 5)$
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