Explanation:
One common binomial that when multiplied results in the difference of two squares is (a + b)(a - b), where a and b are any real numbers. When this binomial is expanded, the middle terms cancel out, leaving only the first and last terms:
(a + b)(a - b) = a^2 - ab + ab - b^2 = a^2 - b^2
For example, (2 + 3)(2 - 3) = 2^2 - 3^2 = -5
Another binomial that can be used is (x + y)^2 - (x - y)^2. When this expression is simplified, it also results in the difference of two squares:
(x + y)^2 - (x - y)^2 = x^2 + 2xy + y^2 - x^2 + 2xy - y^2 = 4xy
For example, if x = 2 and y = 3, then (2 + 3)^2 - (2 - 3)^2 = 5^2 - 1^2 = 24.