Question

Use the distributive property to write an equivalent variable expression.

$- 3 y ( y + 8 )$

Short answer

$- 3y (y + 8) = - 3y^2 - 24y$.

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

Example: $-\text{3} \text{(8} + \text{5} \text{)} = (-\text{3} ) · 8 + (-\text{3} ) · \text{5} = -24-15=- 39$

Step-3:  Use the distributive property to evaluate the expression.

We know that double negative is always positive. $- \text{4} · - \text{7} = + 28$

Distributive Property of Multiplication

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

$\begin{array}{l}-3y(y+8)=-3y·y+(-3y)·8=-3y^2-24y\\ -3y·y=-3y^2\\ -3y(y+8)=-3y^2-24y\end{array}$