Question

Use the distributive property to write an equivalent variable expression.

$6 ( 2p+1 )$

Short answer

$6 (2p+1)= 12p + 6$.

Step-by-step solution

Step-1 – What are real numbers? 

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

Step-2 – Distributive Property of Multiplication 

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

Distributive Property of Multiplication

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

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

Step-3:  Evaluate the expression using the distributive property. 

Distributive Property of Multiplication

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

$\begin{array}{l}6(2p+1)=6·2p+6·1=12p+6\\ 6(2p+1)=12p+6\end{array}$