1. use patterns to multiply special binomials.
Objective
use patterns to multiply special binomials.

2. There are formulas (shortcuts) that work for certain polynomial multiplication problems. (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2 (a - b)(a + b) = a2 - b2
Being able to use these formulas will help you in the future when you have to factor. If you do not remember the formulas, you can always multiply using the distributive property or FOIL.

3. Let’s try one! 1) Multiply: (x + 4)2
You can multiply this by rewriting the binomial squared as (x + 4)(x + 4) and then multiplying it out… OR You can use the following rule as a shortcut: (a + b)2 = a2 + 2ab + b2 For comparison, I’ll show you both ways.

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
+4x
+4x
+16
Now let’s do it with the shortcut!

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. 2) Multiply: (3x + 2y)2 using (a + b)2 = a2 + 2ab + b2
(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 (2a + 3)2
4a2 – 9
4a2 + 9
4a2 + 36a + 9
4a2 + 12a + 9

8. 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

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

10. 5) Multiply (x – 3)(x + 3) x2 +3x -3x -9
This always happens when you multiply a binomial by its conjugate
This always happens when you multiply a binomial by its conjugate
5) Multiply (x – 3)(x + 3) x2
First terms: Outer terms: Inner terms: Last terms: Combine like terms. x2 – 9
Notice the middle terms eliminate each other!
+3x
-3x -9
This is called the difference of squares.

11. 5) 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

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

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