1. Objective: I will be able to:
use patterns to multiply special binomials

2. Special Product Patterns: Square of a Binomial Pattern (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2 Sum and Difference Pattern (a - b)(a + b) = a2 - b2

3. 1. Multiply: (x + 4)2
You can multiply this by rewriting this as (x + 4)(x + 4) OR
You can use the Square of a Binomial Pattern:
(a + b)2 = a2 + 2ab + b2

4. Notice you have two of the same answer
1. Multiply (x + 4)(x + 4)
Notice you have two of the same answer x2
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
x2 +8x + 16 x +4
+4x
+4x x2
+4x
+16
+4x
+16

5. 1. Multiply: (x + 4)2 using (a + b)2 = a2 + 2ab + b2
That’s why the 2 is in the formula!
1. Multiply: (x + 4)2 using (a + b)2 = a2 + 2ab + b2
a is the first term, b is the second term
(x + 4)2
a = x and b = 4
Plug into the formula a2 + 2ab + b2
(x)2 + 2(x)(4) + (4)2
Simplify.
x2 + 8x+ 16
This is the same answer

6. Plug into the formula a2 + 2ab + b2
Guided Practice Multiply: (3x + 2y)2 using Square of a Binomial Pattern
(3x + 2y)2
a = 3x and b = 2y
Plug into the formula a2 + 2ab + b2
(3x)2 + 2(3x)(2y) + (2y)2
Simplify
9x2 + 12xy +4y2

7. Multiply: (x – 5)2 using (a – b)2 = a2 – 2ab + b2
Multiply: (x – 5)2 using (a – b)2 = a2 – 2ab + b2 *Everything is the same except the signs
(x)2 – 2(x)(5) + (5)2
x2 – 10x + 25
4. Multiply: (4x – y)2
(4x)2 – 2(4x)(y) + (y)2
16x2 – 8xy + y2

8. Notice the middle terms eliminate each other!
5. Multiply (x – 3)(x + 3)
Notice the middle terms eliminate each other! x2
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
x2 – 9 x -3 +3
+3x
-3x x2
-3x -9
+3x -9
This is called the difference of squares.

9. Continued… Multiply (x – 3)(x + 3) using (a – b)(a + b) = a2 – b2
*You can only use this rule when the binomials are exactly the same except for the sign.
(x – 3)(x + 3)
a = x and b = 3
(x)2 – (3)2
x2 – 9

10. 6. Multiply: (y – 2)(y + 2) (y)2 – (2)2 y2 – 4
7. Multiply: (5a + 6b)(5a – 6b)
(5a)2 – (6b)2
25a2 – 36b2

11. Independent Practice Multiply (2a + 3)2
4a2 + 36a + 9
4a2 + 12a + 9

12. Multiply (x – y)2
x2 + 2xy + y2
x2 – 2xy + y2
x2 + y2
x2 – y2

13. Multiply (4m – 3n)(4m + 3n) 16m2 – 9n2 16m2 + 9n2 16m2 – 24mn - 9n2