Q49. - Algebra 1

Question

Find the product.

$\left(3r-7t\right)\left(2r+5t\right)$

Step-by-Step Solution

Answer

The final answer is $\mathbf{6}{\mathit{r}}^{\mathbf{2}}\mathbf{+}\mathit{r}\mathit{t}\mathbf{-}\mathbf{35}{\mathit{t}}^{\mathbf{2}}$.

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 ( 3 r − 7 t ) ( 2 r + 5 t ) .

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

$\begin{array}{c}\left(3r-7t\right)\left(2r+5t\right)=3r\left(2r+5t\right)-7t\left(2r+5t\right)\\ =3r\left(2r\right)+3r\left(5t\right)-7t\left(2r\right)-7t\left(5t\right)\\ =6r^2+15rt-14rt-35t^2\\ =6r^2+rt-35t^2\end{array}$

Therefore, the final answer is $6r^2+rt-35t^2$.