5.6 Distributive Property

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

How do you apply the Distributive Property to the expression -3(2c - 5)?

Back

You distribute -3 to both terms inside the parentheses: -3 * 2c + (-3) * (-5) = -6c + 15.

Front

What is the result of applying the Distributive Property to (b + 8)5?

Back

You distribute 5 to both terms: 5 * b + 5 * 8 = 5b + 40.

Front

When simplifying the expression 6(2m + 3) - 4m, what is the first step?

Back

First, apply the Distributive Property: 6 * 2m + 6 * 3 - 4m = 12m + 18 - 4m.

Front

What do you get when you combine like terms in the expression 12m + 18 - 4m?

Back

You combine like terms: 12m - 4m = 8m, so the final expression is 8m + 18.

Front

How do you simplify the expression 5(2y - 3) using the Distributive Property?

Back

Distribute 5 to both terms: 5 * 2y + 5 * (-3) = 10y - 15.

Front

What is the simplified form of 3(x + 4) using the Distributive Property?

Back

Distribute 3 to both terms: 3 * x + 3 * 4 = 3x + 12.

Front

What is a common mistake when applying the Distributive Property?

Back

A common mistake is forgetting to distribute to both terms inside the parentheses or incorrectly applying the signs.

Front

Can the Distributive Property be used with subtraction?

Back

Yes, the Distributive Property can be applied to subtraction as well: a(b - c) = ab - ac.

Front

What is the importance of combining like terms after applying the Distributive Property?

Back

Combining like terms simplifies the expression and makes it easier to understand and solve.