Question

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

$\left(12p^3-11q^2\right)\left(12p^3+11q^2\right)$

Short answer

The solution is$144p^6-121q^4$.

Step-by-step solution

Step 1. Given information.

The given expression is$\left(12p^3-11q^2\right)\left(12p^3+11q^2\right)$.

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

Solve it as follows:

$$\begin{gathered} \left(12p^3-11q^2\right)\left(12p^3+11q^2\right)={\left(12p^3\right)}^2-{\left(11q^2\right)}^2 \\ \Rightarrow 144p^6-121q^4 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is$144p^6-121q^4$.