Question

m6|l19 expanding and factoring
use the distributive property to write equivalent expressions in expanded form.
you can use the boxes to organize your thinking. label the boxes to represent the expression.

8(-3y - 7)
=8(-3y + -7)

Explanation:

Step1: Apply distributive property

The distributive property is \(a(b + c)=ab + ac\). For \(8(-3y + -7)\), we distribute 8 to both terms inside the parentheses.
So, \(8\times(-3y)+8\times(-7)\)

Step2: Calculate each product

Calculate \(8\times(-3y)= -24y\) and \(8\times(-7)= -56\).

Step3: Combine the terms

Combine the two results: \(-24y - 56\)

Answer:

\(8(-3y - 7)= -24y - 56\) (and for the box labeling, the left - most box is \(8\), the top - left box is \(-3y\), the top - right box is \(-7\), the bottom - left rectangle is \(8\times(-3y)\) (or \(-24y\)) and the bottom - right rectangle is \(8\times(-7)\) (or \(-56\)) depending on the box's purpose, but the expanded form is \(-24y - 56\))