Question

Multiply each pair of conjugates using the product of the conjugates pattern.

$\left(15m^2-8n^4\right)\left(15m^2+8n^4\right)$

Short answer

The solution is$225m^4-64n^8$.

Step-by-step solution

Step 1. Given information.

The given expression is$\left(15m^2-8n^4\right)\left(15m^2+8n^4\right)$.

Step 2. Simplify the expression by using the difference of squares a+ba-b=a2-b2

Solve it as follows:

$$\begin{gathered} \left(15m^2-8n^4\right)\left(15m^2+8n^4\right)={\left(15m^2\right)}^2-{\left(8n^4\right)}^2 \\ \Rightarrow 225m^4-64n^8 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is$225m^4-64n^8$.