Simplifying Expressions and Distributive Property

Front

What is the process of combining like terms in an expression?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, in the expression 8a + 4b + 2c - 3b + a, you can combine 8a and a to get 9a, and combine 4b and -3b to get b, resulting in 9a + b + 2c.

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 set of parentheses.

Front

Simplify the expression: 5(a + 6)

Back

5a + 30

Front

What is a coefficient in mathematics?

Back

A coefficient is a number in front of a variable that indicates how many times to multiply the variable. For example, in 4x, 4 is the coefficient.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors. For example, factoring 4x + 10 gives 2(2x + 5).

Front

What is a term in an algebraic expression?

Back

A term is a single mathematical expression that can be a number, a variable, or a combination of both, such as 3x or 5.

Front

What is a constant in an expression?

Back

A constant is a fixed value that does not change. For example, in the expression 3x + 5, the number 5 is a constant.

Front

Simplify the expression: 8a + 4b + 2c - 3b + a

Back

9a + b + 2c

Front

Which expression is equivalent to 4x + 30y?

Back

2(2x + 15y) or 4(x + 15y) are equivalent, but 2(2x + 15y) is a simpler factorization.

Front

What is the result of applying the distributive property to 3(x + 4)?

Back

3x + 12