To square a binomial, multiply the binomial by itself:
(a + b)² = (a + b)(a + b)

The square of a binomial is always the sum of:

1. The first term squared,
2. 2 times the product of the first and second terms, and
3. the second term squared.

When a binomial is squared, the resulting trinomial is called a perfect square trinomial.

Examples:

(x + 5)² = x² +2(x)(5) + 5² = x² + 10x + 25
(100 - 1)² = 100² +2(100)(- 1) + (- 1)² = 10000 - 200 + 1 = 9801
(2x - 3y)² = (2x)² +2(2x)(- 3y) + (- 3y)² = 4x² -12xy + 9y²

When we multiply two polynomials that are the sum and difference of the same 2 terms -- (x + 5) and (x - 5) for example -- we get an interesting result:

The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared. Thus, this resulting binomial is called a difference of squares.

Examples:

(7 - 2)(7 + 2) = 7² -2² = 49 - 4 = 45
(x + 9)(x - 9) = x² -9² = x² - 81
(2x - y)(2x + y) = (2x)² - y² = 4x² - y²
(3x² -2)(3x² +2) = (3x²)² -2² = 9x⁴ - 4
(- y + 5x)(- y - 5x) = (- y)² - (5x)² = y² -15x²