Math7 5.1: Combining Like Terms and Distributive Property

Front

What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 4y are not.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable. For example, 3x + 5x = (3 + 5)x = 8x.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parentheses.

Front

Simplify the expression: 2(x + 3) + 4.

Back

2(x + 3) + 4 = 2x + 6 + 4 = 2x + 10.

Front

What is the first step in simplifying an expression with parentheses?

Back

The first step is to apply the distributive property to eliminate the parentheses.

Front

How do you simplify the expression: 5a + 3b - 2a + 4b?

Back

Combine like terms: (5a - 2a) + (3b + 4b) = 3a + 7b.

Front

What is the result of combining the like terms in the expression: 7x - 2 + 3x + 5?

Back

Combine like terms: (7x + 3x) + (-2 + 5) = 10x + 3.

Front

How do you simplify the expression: 4(2y - 3) + 6?

Back

Apply the distributive property: 4(2y) - 4(3) + 6 = 8y - 12 + 6 = 8y - 6.

Front

What is the simplified form of the expression: 3(4x + 2) - 5x?

Back

3(4x + 2) - 5x = 12x + 6 - 5x = 7x + 6.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to combine like terms and perform any operations to reduce it to its simplest form.