Q61. - Algebra 2

Question

Name the property illustrated by each equation.

 

$3\left(x+12\right)=3x+3\left(12\right)$

Step-by-Step Solution

Answer

The property illustrated by the equation $3\left(x+12\right)=3x+3\left(12\right)$ is distributive property.

Step 1 - Define distributive property

 The distributive property is $a\left(b+c\right)=ab+ac$ or $\left(a+b\right)c=ac+bc$.

Step 2 - State an example

Give an example to illustrate the inverse property of multiplication. Let $a=5$, $b=8$ and $c=2$, then

$\begin{array}{c}5\left(8+2\right)=5\left(10\right)\\ =50\\ 5\left(8\right)+5\left(2\right)=40+10\\ =50\\ 5\left(8+2\right)=5\left(8\right)+5\left(2\right)\end{array}$

Step 3 - State the conclusion

Since it is given that $3\left(x+12\right)=3x+3\left(12\right)$, therefore, it illustrates the distributive property.