Question

1. $16x^2 - 81y^2$

Explanation:

Step1: Recognize difference of squares

Rewrite terms as perfect squares:
$16x^2 = (4x)^2$, $81y^2 = (9y)^2$
So $16x^2 - 81y^2 = (4x)^2 - (9y)^2$

Step2: Apply difference of squares formula

Use $a^2 - b^2 = (a+b)(a-b)$, where $a=4x$, $b=9y$:
$(4x)^2 - (9y)^2 = (4x + 9y)(4x - 9y)$

Answer:

$\boldsymbol{(4x + 9y)(4x - 9y)}$