Question

Use the distributive property to write an equivalent variable expression.

$-5\left(y+4\right)$

Short answer

The equivalent variable expression is $-5y-20$.

Step-by-step solution

Step 1.  Distributive property

For any real numbers a, b, and c, the distributive property is given by:

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

Step 2.  Example of distributive property

To evaluate the expression $3\left(4+t\right)$, distribute 3 to both the terms inside the parenthesis and remove the parenthesis sign to get

$\begin{array}{c}3\left(4+t\right)=3\cdot 4+3\cdot t\\ =12+3t\end{array}$

Step 3.  Rewrite the given expression using distributive property

To write an equivalent variable expression for the given expression $-5\left(y+4\right)$, distribute –5 to both the terms inside the parenthesis and simplify further by multiplying the numbers as shown below

$\begin{array}{c}-5\left(y+4\right)=-5\cdot y-5\cdot 4\\ =-5y-20\end{array}$

Thus, the equivalent variable expression for the given expression is $-5y-20$.