Question

What property is illustrated by the statement: $3(4-9)= 3\left(4\right) - 3\left(9\right)$?

Short answer

The name of the property is distributive property of multiplication. .

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: $\text{12} \text{(7} \text{-} \text{4} \text{)} = \text{12} · \text{7} - \text{12} · \text{4} = 84 - 48 = 36$

Step-3:  What property is illustrated by the statement?

Distributive Property of Multiplication

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

According to the above property, we can write that the name of the property $\text{3} \text{(4} - \text{9} \text{)} = \text{3} \left(4\right) - 3 \left(9\right)$is Distributive Property of Multiplication