Distributive and Factoring Expressions

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.

Front

How do you factor an expression?

Back

To factor an expression, you find the greatest common factor (GCF) of the terms and express the original expression as a product of the GCF and the remaining terms.

Front

What is the greatest common factor (GCF)?

Back

The GCF of two or more numbers is the largest number that divides all of them without leaving a remainder.

Front

Factor the expression: 6x + 20.

Back

2(3x + 10) is the factored form.

Front

What is the result of applying the distributive property to 5(a + 6)?

Back

5a + 30 is the result of distributing 5 across the sum.

Front

How do you identify the GCF of 18 and 45?

Back

The GCF of 18 and 45 is 9, as it is the largest number that divides both 18 and 45.

Front

Factor the expression: 12x - 20.

Back

4(3x - 5) is the factored form.

Front

Factor the expression: 8x - 10.

Back

2(4x - 5) is the factored form.

Front

What is the purpose of factoring in algebra?

Back

Factoring simplifies expressions and helps solve equations by breaking them down into simpler components.

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 it in standard form.