Question

find the product using a special product formula.
$(x^3y^3 - 2xy^3)(x^3y^3 + 2xy^3)$

$(x^3y^3 - 2xy^3)(x^3y^3 + 2xy^3) = \square$ (simplify your answer.)

Explanation:

Step1: Recognize difference of squares

The expression matches $(a-b)(a+b)=a^2-b^2$, where $a=x^3y^3$, $b=2xy^3$.

Step2: Compute $a^2$

$a^2=(x^3y^3)^2 = x^{6}y^{6}$

Step3: Compute $b^2$

$b^2=(2xy^3)^2 = 4x^2y^{6}$

Step4: Subtract $b^2$ from $a^2$

$a^2 - b^2 = x^6y^6 - 4x^2y^6$

Answer:

$x^6y^6 - 4x^2y^6$