Question

1. $12x^{2}-27y^{2}$

Explanation:

Step1: Factor out the GCF

$12x^2 - 27y^2 = 3(4x^2 - 9y^2)$

Step2: Apply difference of squares

$4x^2 - 9y^2 = (2x)^2 - (3y)^2 = (2x-3y)(2x+3y)$

Step3: Combine factors

$3(2x-3y)(2x+3y)$

Answer:

$3(2x - 3y)(2x + 3y)$