Adding, Subtracting, and Multiplying Polynomials - Killingly Public

6.3

Adding, Subtracting, and Multiplying Polynomials Goals p Add, subtract, and multiply polynomials. p Use polynomial operations in real-life problems.

Your Notes

Example 1

a.

Adding Polynomials Vertically and Horizontally

2x3
3x2  7x
5  3x3  2x2
3x 5x 3
x 2  4x
5

b. (x3  6x  4)  (
6x3  2x2
9x
2)  x 3
6x 3  2x2  6x
9x  4
2 
5x 3  2x2
3x  2

Example 2

a.

Subtracting Polynomials Vertically and Horizontally

7x3  4x2
x
4

7x 3  4x2
x
4


(5x3
x2  x
6)


5x 3  x2
x  6 2x3  5x2
2x  2

b. (3x4  9x3  2)
(2x4  6x3  2x
4)  3x4  9x3  2
2x 4
6x 3
2x  4  x 4  3x 3
2x  6

Example 3

Multiplying Polynomials Vertically

x2
x  3  x2 2x 2
2x  6

130

Multiply x2 ⴚ x ⴙ 3 by 2.

x 3
x 2  3x

Multiply x2 ⴚ x ⴙ 3 by x.

x3  x2  x  6

Combine like terms.

Algebra 2 Notetaking Guide • Chapter 6

Your Notes

Example 4

Multiplying Polynomials Horizontally

Multiply the polynomials. (x
2)(3x2
x  5)  (x
2) 3x 2
(x
2) x  (x
2) 5  3x 3
6x2
x2  2x  5x
10  3x 3
7x2  7x
10

Example 5

Multiplying Three Binomials

Multiply the polynomials. (x  2)(x
1)(x
3)  ( x2  x
2 )(x
3)  ( x2  x
2 )(x)
( x 2  x
2 )(3)  x 3  x2
2x
3x2
3x  6  x 3
2x2
5x  6

SPECIAL PRODUCT PATTERNS Sum and Difference

Example

(a  b)(a
b)  a2
b2

(x  3)(x
3)  x2
9

Square of a Binomial (a  b)2  a2  2ab  b2

(y  4)2  y2  8y  16

(a
b)2  a2
2ab  b2

(3t 2
2)2  9t 4
12t 2  4

Cube of a Binomial (a  b)3

(x  1)3

 a3  3a2b  3ab2  b3 (a
b)3

 x3  3x2  3x  1 (p
2)3

 a3
3a2b  3ab2
b3

 p3
6p 2  12p
8

Lesson 6.3 • Algebra 2 Notetaking Guide

131

Your Notes

Example 6

Using Special Product Patterns

Multiply the polynomials. a. (3z  4)(3z
4)  ( 3z )2
4

2

 9z2
16 b. (4x2  3y)2  ( 4x2 )2  2( 4x2 )( 3y )  ( 3y )2  16x 4  24x2y  9y 2 c. (cd
4)3  ( cd )3
3( cd )2( 4 )  3( cd )( 4 )2
4  c 3d 3
12c 2d 2  48cd
64

Checkpoint Complete the following exercises.

1. Add (
3x2  3x
7)  (x2
9x  5).


2x2
6x
2 2. Subtract (6x3  x2  1)
(2x3
6x  3).

4x3  x2  6x
2 3. Multiply (x
3)(x  1)(x  7).

Homework

x3  5x2
17x
21 4. Multiply (2w
3)2.

4w2
12w  9

132

Algebra 2 Notetaking Guide • Chapter 6

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