Difference of squares

Definition

A difference of squares is an expression in the form $a^2 - b^2$ which can be factored into $(a + b)(a - b)$. It represents the subtraction of one squared term from another.

5 Must Know Facts For Your Next Test

1. A difference of squares can always be factored into two binomials.
2. The general form is $a^2 - b^2 = (a + b)(a - b)$.
3. It is applicable only when both terms are perfect squares.
4. This method is useful for solving quadratic equations and simplifying expressions.
5. The middle terms cancel out, resulting in no linear term in the expanded form.

Review Questions

• What is the factored form of $x^2 - 16$?
• How do you factor the expression $9y^2 - 25$?
• Why does $x^2 + 4$ not qualify as a difference of squares?

Related terms

Perfect Square: A number or expression that can be expressed as the square of an integer or another expression.

Quadratic Equation: An equation that can be written in the standard form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Factoring: The process of breaking down an expression into a product of simpler expressions.