Question

1. 7x³y - 63xy³

Explanation:

Step1: Factor out GCF

Identify and factor the greatest common factor of the two terms.
$7x^3y - 63xy^3 = 7xy(x^2 - 9y^2)$

Step2: Apply difference of squares

Recognize $x^2 - 9y^2$ as a difference of squares and factor it.
$x^2 - 9y^2 = x^2 - (3y)^2 = (x - 3y)(x + 3y)$

Step3: Combine factors

Substitute the factored form back into the expression.
$7xy(x - 3y)(x + 3y)$

Answer:

$7xy(x - 3y)(x + 3y)$