Distributive Property and Combining Like Terms

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

What is a coefficient in an algebraic expression?

Back

A coefficient is a numerical factor that multiplies a variable in an algebraic expression, such as the '3' in '3n'.

Front

How do you combine like terms in an expression?

Back

To combine like terms, you add or subtract the coefficients of terms that have the same variable raised to the same power.

Front

What is an example of combining like terms?

Back

In the expression n - 10 + 9n - 3, you combine 'n' and '9n' to get '10n', and '-10' and '-3' to get '-13', resulting in '10n - 13'.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of their variables.

Front

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

Back

Using the Distributive Property, you multiply 3 by each term inside the parentheses: 3 * 2c = 6c and 3 * -5 = -15, resulting in 6c - 15.

Front

What is the result of simplifying -8 - 9(2x + 5)?

Back

First, apply the Distributive Property: -9 * 2x = -18x and -9 * 5 = -45. Then combine: -8 - 45 = -53, resulting in -18x - 53.

Front

What is the result of simplifying 8(5f - 7) + 3f?

Back

First, apply the Distributive Property: 8 * 5f = 40f and 8 * -7 = -56. Then combine with 3f: 40f + 3f = 43f, resulting in 43f - 56.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power, such as 2x and 5x.

Front

What is the first step in solving an expression with the Distributive Property?

Back

The first step is to identify the term outside the parentheses and distribute it to each term inside the parentheses.