Question

Find the product.

$\left(x-3\right)\left(x+7\right)$

Short answer

The final answer is${\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\mathit{x}\mathbf{-}\mathbf{21}$

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 (x−3)(x+7) .

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

$\begin{array}{c}\left(x-3\right)\left(x+7\right)=x\left(x+7\right)-3\left(x+7\right)\\ =x\left(x\right)+x\left(7\right)-3\left(x\right)-3\left(7\right)\\ =x^2+7x-3x-21\\ =x^2+4x-21\end{array}$

Therefore, the final answer is$x^2+4x-21$.