Question

1. $(x - y)(x^2 + 2xy + y^2) =$

Explanation:

Step1: Distribute each term

Multiply $x$ and $-y$ by the trinomial.
$$(x)(x^2+2xy+y^2) - y(x^2+2xy+y^2)$$

Step2: Expand each product

Calculate the product for each part.
$$x^3 + 2x^2y + xy^2 - x^2y - 2xy^2 - y^3$$

Step3: Combine like terms

Add/subtract terms with the same variables.
$$x^3 + (2x^2y - x^2y) + (xy^2 - 2xy^2) - y^3 = x^3 + x^2y - xy^2 - y^3$$

Answer:

$x^3 + x^2y - xy^2 - y^3$