Chapter 8.4, Problem 38PPS

To determine

To find: The product ${\left(5x^2-y^2\right)}^2$

Answer to Problem 38PPS

  $25x^4-10x^2{y}^2+y^4$

Explanation of Solution

Given:

  ${\left(5x^2-y^2\right)}^2$

Calculation:

The given expression is ${\left(5x^2-y^2\right)}^2$

Apply the formula ${\left(a-b\right)}^2=a^2-2ab+b^2$ and then simplify

  $\begin{array}{l}{\left(5x^2-y^2\right)}^2\\ ={\left(5x^2\right)}^2-2\cdot 5x^2\cdot y^2+{\left(y^2\right)}^2\\ =25x^4-10x^2{y}^2+y^4\end{array}$