1. = (7y2 + 5y2) + [2y + (–4y) + [(– 3) + 2] Group like terms.
Add Polynomials
A. Find (7y2 + 2y – 3) + (2 – 4y + 5y2).
Horizontal Method
(7y2 + 2y – 3) + (2 – 4y + 5y2)
= (7y2 + 5y2) + [2y + (–4y) + [(– 3) + 2] Group like terms.
= 12y2 – 2y – 1 Combine like terms.
Example 1

2. Notice that terms are in descending order with like terms aligned.
Add Polynomials
Vertical Method
7y2 + 2y – 3
(+) 5y2 – 4y + 2
Notice that terms are in descending order with like terms aligned.
12y2 – 2y – 1
Answer: 12y2 – 2y – 1
Example 1

3. = [4x2 + (–7x2)] + [(–2x) + 3x] + [7 + (–9)] Group like terms.
Add Polynomials
B. Find (4x2 – 2x + 7) + (3x – 7x2 – 9).
Horizontal Method
(4x2 – 2x + 7) + (3x – 7x2 – 9)
= [4x2 + (–7x2)] + [(–2x) + 3x] + [7 + (–9)] Group like terms.
= –3x2 + x – 2 Combine like terms.
Example 1

4. Align and combine like terms.
Add Polynomials
Vertical Method
4x2 – 2x + 7
(+) –7x2 – 3x – 9
–3x2 + x – 2
Align and combine like terms.
Answer: –3x2 + x – 2
Example 1

5. A B C D A. Find (3x2 + 2x – 1) + (–5x2 + 3x + 4). A. –2x2 + 5x + 3
B. 8x2 + 6x – 4
C. 2x2 + 5x + 4
D. –15x2 + 6x – 4 A B C D
Example 1

6. A B C D B. Find (4x3 + 2x2 – x + 2) + (3x2 + 4x – 8). A. 5x2 + 3x – 6
B. 4x3 + 5x2 + 3x – 6
C. 7x3 + 5x2 + 3x – 6
D. 7x3 + 6x2 + 3x – 6 A B C D
Example 1

7. A. Find (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2).
Subtract Polynomials
A. Find (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2).
Horizontal Method
Subtract 9y4 – 7y + 2y2 by adding its additive inverse.
(6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)
= (6y2 + 8y4 – 5y) + (–9y4 + 7y – 2y2)
= [8y4 + (–9y4)] + [6y2 + (–2y2)] + (–5y + 7y)
= –y4 + 4y2 + 2y
Example 2

8. Subtract Polynomials
Vertical Method
Align like terms in columns and subtract by adding the additive inverse.
8y4 + 6y2 – 5y
(–) 9y4 + 2y2 – 7y
8y4 + 6y2– 5y
(+) –9y4 – 2y2 + 7y
–y4 + 4y2 + 2y
Add the opposite.
Answer: –y4 + 4y2 + 2y
Example 2

9. Subtract 4n4 – 3 + 5n2 by adding the additive inverse.
Subtract Polynomials
Find (6n2 + 11n3 + 2n) – (4n – 3 + 5n2).
Horizontal Method
Subtract 4n4 – 3 + 5n2 by adding the additive inverse.
(6n2 + 11n3 + 2n) – (4n – 9 + 5n2)
= (6n2 + 11n3 + 2n) + (–4n + 3 – 5n2 )
= 11n3 + [6n2 + (–5n2)] + [2n + (–4n)] + 3
= 11n3 + n2 –2n + 3
Answer: 11n3 + n2 – 2n + 3
Example 2

10. Subtract Polynomials
Vertical Method
Align like terms in columns and subtract by adding the additive inverse.
11n3 + 6n2 + 2n + 0
(–) 0n3 + 5n2 + 4n – 3
11n3 + 6n2 + 2n + 0
(+) 0n3 – 5n2 – 4n + 3
11n3 + n2 – 2n + 3
Add the opposite.
Answer: 11n3 + n2 – 2n + 3
Example 2

11. A B C D A. Find (3x3 + 2x2 – x4) – (x2 + 5x3– 2x4). A. 2x2 + 7x3 – 3x4
B. x4 – 2x3 + x2
C. x2 + 8x3 – 3x4
D. 3x4 + 2x3 + x2 A B C D
Example 2

12. A B C D B. Find (8y4 + 3y2 – 2) – (6y4 + 5y3 + 9). A. 2y4 – 2y2 – 11
B. 2y4 + 5y3 + 3y2 – 11
C. 2y4 – 5y3 + 3y2 – 11
D. 2y4 – 5y3 + 3y2 + 7 A B C D
Example 2

13. A. Write an equation that represents the sales of video games V.
Add and Subtract Polynomials
A. VIDEO GAMES The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V and sales of traditional toys R. In recent years, the sales of traditional toys and total sales could be modeled by the following equations, where n is the number of years since 2000.
R = 0.46n n2 + 3n + 19
T = 0.45n n n
A. Write an equation that represents the sales of video games V.
Example 3

14. Find an equation that models the sales of video games V.
Add and Subtract Polynomials
Find an equation that models the sales of video games V.
Subtract the polynomial for R from the polynomial for T.
video games + traditional toys = total toy sales
V + R = T
V = T – R
0.46n n2 – 3n – 19
(–)0.45n n2 – 4.4n – 22.6
–0.01n n n
Example 3

15. Add and Subtract Polynomials
0.46n n2 – 3n – 19
(+) –0.45n3 – 1.85n n
–0.01n n n + 3.6
Add the opposite.
Answer: V = –0.01n n n + 3.6
Example 3

16. Add and Subtract Polynomials
B. Use the equation to predict the amount of video game sales in the year 2009?
The year 2009 is 2009 – 2000 or 9 years after the year Substitute 9 for n.
V = –0.01(9) (9) (9) + 3.6
= –
= 12.96
Answer: The amount of video game sales in 2009 will be billion dollars.
Example 3

17. A B C D A. 50x2 – 50x + 500 B. –50x2 – 50x + 500 C. 250x2 + 950x + 500
A. BUSINESS The profit a business makes is found by subtracting the cost to produce an item C from the amount earned in sales S. The cost to produce and the sales amount could be modeled by the following equations, where x is the number of items produced. C = 100x x – 300 S = 150x x Find an equation that models the profit. A B C D
A. 50x2 – 50x + 500
B. –50x2 – 50x + 500
C. 250x x + 500
D. 50x x + 100
Example 3

18. B. Use the equation 50x2 – 50x + 500 to predict the profit if 30 items are produced and sold.
Example 3