Difference of Squares
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The difference of squares is a specific algebraic identity that describes the result of subtracting one square from another. It states that the difference between two squared terms can be factored as the product of the sum and the difference of the terms.
The difference of squares formula is:
Explanation:
a^2 and b^2 are perfect squares (squares of terms a and b).
The expression a^2 - b^2 can be factored into two binomials: a + b and a - b.
Example:
For x^2 - 9, this is a difference of squares because:
Key Characteristics:
The terms must be perfect squares (e.g., a^2 and b^2).
The operation involved is subtraction (hence "difference").
The difference of squares identity is often used to simplify algebraic expressions and solve equations more easily.