1. 6.3 Adding, Subtracting, &
Multiplying Polynomials
p. 338

2. To + or - , + or – the coeff. of like terms!
Vertical format :
Add 3x3+2x2-x-7 and x3-10x2+8.
3x3 + 2x2 – x – 7
+ x3 – 10x2 + 8 Line up like terms
4x3 – 8x2 – x + 1

3. Horizontal format : Combine like
terms
(8x3 – 3x2 – 2x + 9) – (2x3 + 6x2 – x + 1)=
(8x3 – 2x3)+(-3x2 – 6x2)+(-2x + x) + (9 – 1)=
6x3 + -9x2 + -x + 8 =
6x3 – 9x2 – x + 8

4. Examples: Adding & Subtracting
(9x3 – 2x + 1) + (5x2 + 12x -4) =
9x3 + 5x2 – 2x + 12x + 1 – 4 =
9x3 + 5x2 + 10x – 3
(2x2 + 3x) – (3x2 + x – 4)=
2x2 + 3x – 3x2 – x + 4 =
2x2 - 3x2 + 3x – x + 4 =
-x2 + 2x + 4

5. Multiplying Polynomials: Vertically
(-x2 + 2x + 4)(x – 3)=
-x2 + 2x + 4
* x–3
3x2 – 6x – 12
-x3 + 2x2 + 4x
-x3 + 5x2 – 2x – 12

6. Multiplying Polynomials :
Horizontally
(x – 3)(3x2 – 2x – 4)=
(x – 3)(3x2)
+ (x – 3)(-2x)
+ (x – 3)(-4) =
(3x3 – 9x2) + (-2x2 + 6x) + (-4x + 12) =
3x3 – 9x2 – 2x2 + 6x – 4x +12 =
3x3 – 11x2 + 2x + 12

7. Multiplying 3 Binomials :
(x – 1)(x + 4)(x + 3) =
FOIL the first two:
(x2 – x +4x – 4)(x + 3) =
(x2 + 3x – 4)(x + 3) =
Then multiply the trinomial by the binomial
(x2 + 3x – 4)(x) + (x2 + 3x – 4)(3) =
(x3 + 3x2 – 4x) + (3x2 + 9x – 12) =
x3 + 6x2 + 5x - 12

8. Some binomial products appear so much
we need to recognize the patterns!
Sum & Difference (S&D):
(a + b)(a – b) = a2 – b2
Example: (x + 3)(x – 3) = x2 – 9
Square of Binomial:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2

9. Last Pattern
Cube of a Binomial
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 - 3a2b + 3ab2 – b3

10. Example:
(x + 5)3 =
a = x and b = 5
x3 + 3(x)2(5) + 3(x)(5)2 + (5)3 =
x3 + 15x2 + 75x + 125