Difference of squares

Definition

The difference of squares is a specific type of polynomial that takes the form $a^2 - b^2$, which can be factored into $(a + b)(a - b)$. It is based on the property that the product of a sum and a difference of two terms results in the difference of their squares.

5 Must Know Facts For Your Next Test

1. The general form is $a^2 - b^2 = (a + b)(a - b)$.
2. It involves two squared terms with a subtraction between them.
3. Recognizing this pattern helps simplify polynomial expressions.
4. It can be used to solve equations by factoring.
5. The factors are always binomials consisting of the sum and difference of the square roots of each term.

Review Questions

• What is the factored form of $x^2 - 16$?
• How do you recognize a difference of squares in a polynomial?
• Why can't $x^2 + y^2$ be factored using the difference of squares method?

Related terms

Perfect Square Trinomial:

A trinomial that can be written as $(a+b)^2$ or $(a-b)^2$, which expands to $a^2 \pm 2ab + b^2$.

Factoring:

The process of breaking down an expression into products of simpler expressions, often used to simplify polynomials.

Binomial:

A polynomial with exactly two terms, such as $ax + b$.