Question

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.When using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change.

Please help

Answer 1

This is sometimes true because when distributing the sign could either be either minus or plus...

If you multiply a positive number with a negative number it will be negative. If you multiply a negative by a negative it will be positive. If you multiply a positive with a positive it will be positive.

Answer 2

Always

Explanation:

While using the distributive property, if the term outside the parenthesis is negative, then the sign of each term inside the parentheses will get change always.

For example, -1(27 - 55) = -27 + 55

It is because of the reason, when we multiply two numbers:

(positive number ( + )) × (positive number ( + )) = (positive number ( + ))

(positive number ( + )) × (negative number ( - )) = (negative number ( - ))

(negative number ( - )) × (positive number ( + )) = (negative number ( - ))

(negative number ( - )) × (negative number ( - )) = (positive number ( + ))