Question

what is the factored form of $x^2y^3 - 2y^3 - 2x^2 + 4$?
$(x^2y^3 + 4) - 2(y^3 + x^2)$
$y^3(x^2 - 2) + 2(-x^2 + 2)$
$(y^3 - 2)(x^2 + 2)$
$(x^2 - 2)(y^3 - 2)$

Explanation:

Step1: Group Terms

Group the first two terms and the last two terms: $(x^2y^3 - 2y^3) + (-2x^2 + 4)$

Step2: Factor Out GCF from Each Group

Factor out $y^3$ from the first group: $y^3(x^2 - 2)$
Factor out $-2$ from the second group: $-2(x^2 - 2)$
Now the expression is $y^3(x^2 - 2) - 2(x^2 - 2)$

Step3: Factor Out Common Binomial

Factor out $(x^2 - 2)$: $(x^2 - 2)(y^3 - 2)$

Answer:

D. $(x^2 - 2)(y^3 - 2)$ (assuming the last option is D, following the order of the options presented)