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 factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, including any common factors and irreducible polynomials.

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 two or more terms inside parentheses.

Front

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

Back

To factor out the GCF, identify the largest factor that divides all terms in the expression and rewrite the expression as the GCF multiplied by the remaining terms.

Front

Factor the expression: 12x + 16.

Back

4(3x + 4).

Front

What is the result of expanding the expression: 3(x + 4)?

Back

3x + 12.

Front

Back

6x + 10 - 4 = 6x + 6.

Front

What is the result of factoring the expression: 20x^2 + 15x?

Back

5x(4x + 3).

Front

Back

-6x + 8.

Front

Back

(x - 3)(x + 3).