1. Multiplying Binomials
Mentally

2. The Distributive Property
(x + 5)(2x + 6)
(x+5) 2x + (x+5)6
2x(x+5) +6(x+5)
2x² + 10x + 6x + 30
2x² + 16x +30
NOTE : Since there are THREE terms this is called a TRINOMIAL

3. Trinomials Multiplying MOST binomials results in THREE terms
You can learn to multiply binomials in your head by using a method called
F O I L

4. The FOIL Method (x + 4)(x +2) first terms last terms (x + 4) ( x + 2)
inner terms
outer terms

5. (x + 4) ( x + 2)
Now write the products
x² x x
first outer inner last
terms terms terms terms

6. To Multiply any two binomials and write the result as a TRINOMIAL follow these steps
multiply the first two terms
multiply the two outer terms
multiply the two inner terms
multiply the last two terms

7. Special Cases There are several special cases of multiplying binomials
Difference of Squares
Perfect Square Trinomials

8. Difference of two squares
When you multiply the sum of two terms and the difference of two terms you get a BINOMIAL
(a + b) (a – b) = a² - b²
This binomial is the difference of two squares

9. A Closer Look (k – 4) (k + 4) Using FOIL k ² + 4k - 4k - 16 k ² - 16
(6c – 3) ( 6c + 3)
36c² +18c – 18c – 9

10. Squaring A Binomial
When you square any binomial(that is multiply it by itself) you get a TRINOMIAL
(x+9)² means (x+9)(x+9)
Using FOIL
x² + 9x + 9x + 81
x² + 18x +81
This is called a PERFECT SQUARE TRINOMIAL

11. REMEMBER: The square of a binomial is the sum of three things:
The square of the first term
Twice the product of the terms
The square of its last term

12. Perfect Square Trinomials
(3x – 6 )² = (3x - 6) (3x – 6)
9x² – 36 x + 36
(2m –4)² = (2m - 4)( 2m – 4)
4m² –16m + 16

13. An example (6x + 3)² The square of the first term: 36 x²
Twice the product of the terms
2( 6x • 3) x
The square of the last terms
(3)(3) +9
36x² x + 9

14. Perfect Square Trinomial patterns
(a + b)² = a² + 2ab + b²
( a – b)² = a ² - 2ab + b²