Q. 273 - Intermediate Algebra

Question

In the following exercises , simplify the equation $\left(2x^2\hspace{0.17em}-\hspace{0.17em}3y^4\right)\left(2x^2\hspace{0.17em}+\hspace{0.17em}3y^4\right)$.

Step-by-Step Solution

Answer

The simplified expression is $4x^4-9y^8$.

Step 1. Given Information.

The expression is $\left(2x^2\hspace{0.17em}-\hspace{0.17em}3y^4\right)\left(2x^2\hspace{0.17em}+\hspace{0.17em}3y^4\right)$.

Step 2. Simplify given equation.

Simplifying $\left(2x^2\hspace{0.17em}-\hspace{0.17em}3y^4\right)\left(2x^2\hspace{0.17em}+\hspace{0.17em}3y^4\right)$

Apply Difference of two squares formula:-

$$\begin{gathered} \left(a-b\right)\left(a+b\right)=a^2-b^2 \\ \left(2x^2-3y^4\right)\left(2x^2+3y^4\right)={\left(2x^2\right)}^2-{\left(3y^4\right)}^2 \\ {\left(2x^2\right)}^2-{\left(3y^4\right)}^2=4x^4-9y^8 \end{gathered}$$