Expanding and Factoring Expressions

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What does it mean to expand an expression?

Back

Expanding an expression means to multiply out the factors and combine like terms to write the expression in its simplest form.

Front

Factor completely: 12x + 8y - 4z

Back

4(3x + 2y - z)

Front

Factor using a negative factor: -10m - 35

Back

-5(2m + 7)

Front

Which of the following is equivalent to 5(2x + 6)?

Back

10x + 30

Front

Factor: 16x + 24x^2

Back

8x(2 + 3x)

Front

Factor in simplest form: 6x + 12

Back

6(x + 2)

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you identify the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers share. To find it, list the factors of each number and identify the largest one they have in common.