Perfect Square Binomial
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
A perfect square binomial is a binomial (an algebraic expression with two terms) that is the square of a binomial. In other words, it is a binomial that results from squaring a binomial expression.
The general form of a perfect square binomial is:
(a + b)^2 or (a - b)^2
When expanded, these forms follow a specific pattern:
1. For (a + b)^2:
(a + b)^2 = a^2 +2ab +b^2
2. For (a - b)^2:
(a - b)^2 = a^2 -2ab +b^2
Key Characteristics:
The square of the first term (a^2),
Twice the product of the two terms (+2ab or -2ab),
The square of the second term (b^2).
Examples of Perfect Square Binomials:
(x + 3)^2 = x^2 + 6x + 9
(2x - 5)^2 = 4x^2 -20x +25
A perfect square binomial is useful in algebraic factorization and simplification processes, where recognizing and expanding such expressions is important.