Question

1. $2x^3 + x^2y - 6xy^2 - 3y^3$

Explanation:

Step1: Group terms

Group the first two terms and the last two terms: $(2x^{3}+x^{2}y)+(-6xy^{2}-3y^{3})$

Step2: Factor out GCF from each group

Factor out $x^{2}$ from the first group and $-3y^{2}$ from the second group: $x^{2}(2x + y)-3y^{2}(2x + y)$

Step3: Factor out the common binomial factor

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

Answer:

$\boldsymbol{(2x + y)(x^{2}-3y^{2})}$