Multiplying Special Binomials

1. Multiplying Binomials
Mentally

2. Special Cases
There are two types special cases of
multiplying binomials
1. Difference of Squares
2. Perfect Square Trinomials

3. 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

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

5. YOU TRY SOME!!!
#1 (x+4)(x-4)
x²-16
#2 (y-8)(y+8)
y²-64
#3 (3a+5)(3a-5)
9a²-25
#4 (m²+k)(m²-k)
m4-k2

6. 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 Distribution/FOIL/Box
x² + 9x + 9x + 81
x² + 18x +81
This is called a PERFECT SQUARE
TRINOMIAL

7. 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

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

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

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

11. YOU TRY SOME!!!
#1 (x+3)(x+3)
x2 + 6x + 9
#2 (y+6)2
y2 + 12y + 36
#3 (k-10)2
k2 - 20k + 100
#4 (4p+q)2
16p2 + 8pq + q2

12. LET’S PUT IT ALL
TOGETHER!
#1 (x+1)(x-1)
#2 (5x+4)(5x+4)
#3 (6y+2)2
#4 (x+4)(x+5)
#5 (y-2)(x-2)