Distributing and Combining Like Terms

Front

What does it mean to distribute in algebra?

Back

To distribute means to multiply a term by each term inside a set of parentheses. For example, in the expression a(b + c), you would calculate ab + ac.

Front

How do you combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 3x + 4x = 7x.

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 in a polynomial.

Front

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

Back

The simplified expression is 2x + 6 + 4 = 2x + 10.

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power. For example, 5x and 2x are like terms, while 5x and 5y are not.

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 distributing -4 in the expression -4(k - 7)?

Back

The result is -4k + 28.

Front

How do you simplify the expression: 3(2x + 4) + 4(x - 5)?

Back

Distributing gives 6x + 12 + 4x - 20. Combining like terms results in 10x - 8.

Front

What is the first step in simplifying the expression -6x + 4(x - 3)?

Back

The first step is to distribute the 4: -6x + 4x - 12.

Front

What is the simplified form of 8a + 6 + 1 + 8a - 3b + b?

Back

Combine like terms: 8a + 8a - 3b + b + 6 + 1 = 16a - 2b + 7.