Question

In the following exercises, find the product of $\left(x^2\hspace{0.17em}+\hspace{0.17em}8y\right)\left(8x\hspace{0.17em}-\hspace{0.17em}{y}^2\right)$.

Short answer

The product of$\left(x^2+8y\right)\left(8x-y^2\right)$is role="math" localid="1644393429702" $8x^3-x^2{y}^2+64xy-8y^3$ .

Step-by-step solution

Step 1. Given Information

The given expression is $\left(x^2+8y\right)\left(8x-y^2\right)$.

Step 2. Solve for the multiplication of given expression.

Multiply the expression $\left(x^2+8y\right)\left(8x-y^2\right)$.

$$\begin{gathered} \left(x^2+8y\right)\left(8x-y^2\right)=x^2·\hspace{0.17em}8x+x^2\left(-y^2\right)+8y·\hspace{0.17em}8x+8y\left(-y^2\right) \\ {x}^2·\hspace{0.17em}8x+x^2\left(-y^2\right)+8y·\hspace{0.17em}8x+8y\left(-y^2\right)=8x^3-x^2{y}^2+64xy-8y^3 \end{gathered}$$