Chapter 7, Problem 3CR

To determine

Expression $\left(y+3\right)7$ as equivalent algebraic expression

Answer to Problem 3CR

An equivalent algebraic expression is $7y+21$

Explanation of Solution

Given information:

The expression, $\left(y+3\right)7$

Concept used:

• The distributive property of binomials (FOIL):

    $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$

• Left Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression, use the left distributive property and simplify the like terms as shown below

  $\begin{array}{c}\left(y+3\right)7\\ =7\cdot y+7\cdot 3\\ =7y+21\end{array}$

Thus, the given expression as an equivalent algebraic expression is $7y+21$