Problem 79 - College Algebra

Question

Find each product. $$(x+y)\left(x^{2}-x y+y^{2}\right)$$

Step-by-Step Solution

Answer

\(x^{3}+y^{3}\)

Step 1: Apply the Distributive Property

Multiply each term in \((x+y)\) to each term in \(\left(x^{2}-x y+y^{2}\right)\). That is, Multiply \(x\) to \(x^{2}\), \(-xy\), and \(y^{2}\) separately; And do the same for \(y\). This gives: \(x(x^{2}-xy+y^{2})+y(x^{2}-xy+y^{2})\)

Step 2: Simplify Each Term

Simplify the expression by applying multiplication to each term. This yields: \(x^{3}-x^{2}y+xy^{2}+x^{2}y-xy^{2}+y^{3}\)

Step 3: Further Simplify by Combining Like Terms

Combine terms that are alike. This yields: \(x^{3}+y^{3}\)