Question

$9x {}^{2} - 4(x + 2y) {}^{2}$
factorize

Answer 1

$9 {x}^{2} - 4 {(x + 2y)}^{2} \\ \\ = {(3x)}^{2} - {(2(x + 2y))}^{2} \\ \\ = ( {3x)}^{2} - {(2x + 4y)}^{2} \\ \\ = (3x + 2x + 4y)(3x - 2x - 4y) \\ \\ = (5x + 4y)(x - 4y)$

Answer 2

Given Equation is 9x^2 - 4(x + 2y)^2

= > 9x^2 - 4(x^2 + 4xy + 4y^2)

= > 9x^2 - 4x^2 - 16xy - 16y^2

= > 5x^2 - 16xy - 16y^2

= > 5x^2 + 4xy - 20xy - 16y^2

= > x(5x + 4y) - 4y(5x + 4y)

= > (x - 4y)(5x + 4y)

Hope this helps!