Question

Use the distributive property to write an equivalent variable expression.

$5(4k+9)$

Short answer

$5(4k+9)=20k+45$

Step-by-step solution

. What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

. Distributive Property of Multiplication 

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property:$\text{a\hspace{0.17em}\hspace{0.17em}(b\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em}}$

Example: $\text{12\hspace{0.17em}\hspace{0.17em}(3\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}12\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}12\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}}=36+48=84$

.:  Evaluate the expression using the distributive property. 

Distributive Property of Multiplication

Property:$\text{a\hspace{0.17em}\hspace{0.17em}(b\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em}}$

$\begin{array}{l}5(4k+9)=5·4k+5·9=20k+45\\ 5(4k+9)=20k+45\end{array}$