Question

. $64x^{2}y^{2} - 144z^{2}$

Explanation:

Step1: Factor out GCF

Identify and factor out the greatest common factor of 64 and 144, which is 16.
$64x^2y^2 - 144z^2 = 16(4x^2y^2 - 9z^2)$

Step2: Recognize difference of squares

Rewrite the terms inside the parentheses as perfect squares to apply the difference of squares formula $a^2 - b^2=(a-b)(a+b)$.
$4x^2y^2 = (2xy)^2$, $9z^2=(3z)^2$
So $4x^2y^2 - 9z^2=(2xy)^2-(3z)^2$

Step3: Apply difference of squares

Factor the difference of squares expression.
$(2xy)^2-(3z)^2=(2xy-3z)(2xy+3z)$

Step4: Combine all factors

Multiply the GCF with the factored binomials.
$16(2xy-3z)(2xy+3z)$

Answer:

$16(2xy - 3z)(2xy + 3z)$