Question

Find the product.

$\left(3a-2\right)\left(6a+5\right)$

Short answer

The final answer is $\mathbf{18}{\mathit{a}}^{\mathbf{2}}\mathbf{+}\mathbf{3}\mathit{a}\mathbf{-}\mathbf{10}$.

Step-by-step solution

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where,$a$ is any non-zero real number.

Step 3. Calculate the product (3a−2)(6a+5).

Use the power of a product rule to find the product.

$\begin{array}{c}\left(3a-2\right)\left(6a+5\right)=3a\left(6a+5\right)-2\left(6a+5\right)\\ =3a\left(6a\right)+3a\left(5\right)-2\left(6a\right)-2\left(5\right)\\ =18a^2+15a-12a-10\\ =18a^2+3a-10\end{array}$

Therefore, the final answer is$18a^2+3a-10$.