Combining Like Terms/Distributive Property

Front

What does it mean to combine like terms in an expression?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies the expression.

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 simplify the expression -8(5b + 2) - 7(b - 5)?

Back

First, distribute: -40b - 16 - 7b + 35. Then combine like terms: -40b - 7b = -47b and -16 + 35 = 19, resulting in -47b - 19.

Front

Identify the like terms in the expression 3x + 7 - 9x + 24y + 2x^2.

Back

The like terms are 3x and -9x.

Front

What is the result of distributing the negative sign in - (c + v + d + 19)?

Back

The result is -c - v - d - 19.

Front

How do you simplify the expression 2x + 1 + 7x?

Back

Combine like terms: 2x + 7x = 9x, so the simplified expression is 9x + 1.

Front

What is the equivalent expression for (7v - 1)8 using the distributive property?

Back

The equivalent expression is 56v - 8.

Front

What are the steps to simplify an expression with multiple like terms?

Back

1. Identify like terms. 2. Group them together. 3. Add or subtract the coefficients. 4. Write the simplified expression.

Front

How do you recognize like terms in an algebraic expression?

Back

Like terms have the same variable(s) raised to the same power. For example, 2x and 3x are like terms, while 2x and 2y are not.

Front

What is the first step in applying the distributive property?

Back

The first step is to multiply the term outside the parentheses by each term inside the parentheses.