When working with polynomials,the product of two binomials occurs repeatedly. There is a shortcut method for finding these products. Recall that a binomial has just two terms, such as
3x – 4 or 2x + 3. We can find the product of these binomials using the distributive
property as follows.
(3x – 4)(2x + 3) = 3x(2x + 3) – 4(2x + 3)
= 3x (2x) + 3x(3) – 4(2x) – 4 (3)
= 6x2 + 9x – 8x – 12
Find the product of the sum and difference of two terms
Some types of binomial products occur frequently. For example,
the product of the sum and difference of the same two terms, x and y, is
(x + y) (x – y) = x2 – xy + xy – y2 FOIL
= x2 – y2.