Objective: Multiply sums and differences of two terms and learn how to simplify the square of a binomial
When multiplying polynomials, there are two specials cases that require a little more attention: multiplying sums and differences of two binomials and squaring binomials. We call these "special products" because their products always follow the same pattern. Lets first look a the product of a sum and a difference. Two examples of such a problem could be:
A) (x+6)(x-6) B) (4x2 - 7)(4x2 + 7)
By looking at these two examples, you can see that each has nearly identical binomials, only one is a sum of the two terms and the other is a difference. To multiply these we could distribute using the FOIL method. However, we can observe that each product will follow this same rule:
(A + B)(A - B) = A2 - B2
The video below demonstrates this rule in greater detail.
The second special product is the case of a binomial squared, an example being (x - 4)2. To simplify the square of a binomial, we should first rewrite the expression as (x - 4)(x - 4) and then proceed by using the FOIL method to get the product of x2 - 8x +16. However, the square of a binomial also follows a rule that could be used to help simplify the expression:
(A + B)2 = A2 + 2AB + B2
(A - B)2 = A2 - 2AB + B2
The video below demonstrates this special product as well. It is worth noting that both of these special products will becoming increasingly important as you move further into Algebra 1 and learn how to factor.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next unit.