Aim #91: How do we multiply binomials?
Do Now: Sara has two dalmatians, Spot and Dotty. Dotty is 3
years older than Spot.
a) Let x represent Spot's age. Express the product of their
ages as an algebraic expression in simplest form in terms of x.
b) What property was used in part (a)?
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Multiplying Binomials
Ex. #1:
2
x ( x + 2) (x + 3)
3x 2x 6 2
x + 5x + 6
Method 1: Distribution
Step 1: Use the distributive property.
Step 2: Combine like terms!
Method 2: Geometric Model
Ex. #2:
Ex. #3:
(2x - 5)(x - 4)
2
2
(3m - n)(4m - 7n)
2
Special Products
Ex. #4: Product of a Sum and a Difference
a) (5x + 3y)(5x - 3y)
6
Middle "like terms"
are additive inverses
and add to 0.
6
b) (n - 2)(n + 2)
Ex. #5: Squares of Sums and Differences
a) (x + 4)
3
Rewrite the binomial power
as a product of 2 binomials.
Then, multiply the 2
binomials.
2
2
b) (11a - 5)
3
4
5