1. Algebra 1
Section 9.4

2. Multiplying Binomials
The FOIL method is an easily remembered pattern for multiplying two binomials.
(a + b)(c + d)

3. Multiplying Binomials
(a + b)(c + d)
= ac + ad + bc + bd
First terms: ac
Outer terms: ad
Inner terms: bc
Last terms: bd

4. Example 1 Multiply (x + 2)(x + 6). First: x2 Outer: 6x Inner: 2x
Last: 12 x2
+ 6x
+ 2x
+ 12
x2 + 8x + 12

5. Example 2 Multiply (y + 6)(4y – 9). First: 4y2 Outer: -9y Inner: 24y
Last: -54
4y2
– 9y
+ 24y
– 54
4y2 + 15y – 54

6. Multiplying Binomials
The FOIL method can be done mentally. Do not forget to combine any like terms.

7. Example 3
Multiply (3a – 5)(a + 3).
3a2
+ 9a
– 5a
– 15
3a2 + 4a – 15

8. Warning! Be careful when squaring a binomial.
(a + b)2 is not equal to a2 + b2!
The FOIL method can help us to correctly square binomials.

9. Example 4 Multiply (2x – 5)2. = (2x – 5)(2x – 5) 4x2 – 10x – 10x + 25

10. Example 5
The length and width of the pool can be represented by 2x and 3x.
With the walkway, they become (2x + 10) and (3x + 10).
Area = Length × Width

11. Example 4
(2x + 10)(3x + 10)
6x2
+ 20x
+ 30x
+ 100
6x2 + 50x + 100

12. Homework: pp