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Found in: Page 252

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Properties of Real Numbers Use properties of real numbers to write the expression without parentheses.$\mathbf{3}\mathbf{\left(}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{\right)}$

The given expression can be written as $\mathbf{3}\mathbit{x}\mathbf{+}\mathbf{3}\mathbit{y}$.

See the step by step solution

## Step 1. Given information.

The given expression is:

$3\left(x+y\right)$

## Step 2. Write the concept.

According to the distributive property of real numbers, if $\mathbit{a}\mathbf{,}\mathbit{b}\mathbf{,}\mathbit{c}$ are three real numbers, then

$\mathbit{a}\mathbf{\left(}\mathbf{b}\mathbf{+}\mathbf{c}\mathbf{\right)}\mathbf{=}\mathbit{a}\mathbit{b}\mathbf{+}\mathbit{a}\mathbit{c}$

## Step 3. Rewrite the expression.

Using the distributive property of real numbers, the given expression can be rewritten as:

$\begin{array}{l}3\left(x+y\right)=3\left(x\right)+3\left(y\right)\\ =3x+3y\end{array}$

Thus, the given expression can be written as $\mathbf{3}\mathbit{x}\mathbf{+}\mathbf{3}\mathbit{y}$.