1. Page 681 #25-29 Pre-Algebra HOMEWORK Subtracting Polynomials 13-4

2. Pre-Algebra
13-1
Polynomials
Our Learning Goal
Students will be able to classify, simplify, add and subtract polynomials.

3. Pre-Algebra
13-1
Polynomials
Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments.
Learn to classify polynomials by degree and by the number of terms.
Learn to simplify polynomials.
Learn to add polynomials.
Learn to subtract polynomials.
…..and that’s all folks!

4. Today’s Learning Goal Assignment
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Subtracting Polynomials
Today’s Learning Goal Assignment
Learn to subtract polynomials.
Pre-Algebra

5. Subtracting Polynomials
13-4
Subtracting Polynomials
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

6. Subtracting Polynomials
13-4
Subtracting Polynomials
Warm Up
Write the opposite of each integer.
1. 10
Subtract.
3. 19 – (–12)
Add.
5. (3x2 + 7) + (x2 – 3x)
6. (2m2 – 3m) + (–5m2 + 2)
–10
2. –7 7 31
4. –16 – 21
–37
4x2 – 3x + 7
–3m2 – 3m + 2
Pre-Algebra

7. Subtracting Polynomials
13-4
Subtracting Polynomials
Problem of the Day
Tara has 4 pairs of shorts, 3 tops, and 2 pairs of sandals. If she wants to wear a completely different outfit than she wore yesterday, how many combinations does she have to choose from? 6
Pre-Algebra

8. Subtracting Polynomials
13-4
Subtracting Polynomials
Learn to subtract polynomials.
Pre-Algebra

9. Subtracting Polynomials
13-4
Subtracting Polynomials
Subtraction is the opposite of addition. To
subtract a polynomial, you need to find its
opposite.
Pre-Algebra

10. Additional Example 1A & 1B: Finding the Opposite of a Polynomial
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Subtracting Polynomials
Additional Example 1A & 1B: Finding the Opposite of a Polynomial
Find the opposite of each polynomial.
A. 8x3y4z2
–(8x3y4z2)
–8x3y4z2
The opposite of a is –a.
B. –3x4 + 8x2
–(–3x4 + 8x2)
3x4 – 8x2
Distribute the sign.
Pre-Algebra

11. Insert Lesson Title Here
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Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 1A & 1B
Find the opposite of each polynomial.
A. 4d2e3f3
–(4d2e3f3)
–4d2e3f3
The opposite of a is –a.
B. –4a2 + 4a4
–(–4a2 + 4a4)
4a2 – 4a4
Distribute the sign.
Pre-Algebra

12. Additional Example 1C: Finding the Opposite of a Polynomial
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Subtracting Polynomials
Additional Example 1C: Finding the Opposite of a Polynomial
Find the opposite of the polynomial.
A. 9a6b4 + a4b2 – 1
–(9a6b4 + a4b2 – 1)
–9a6b4 – a4b2 + 1
Distribute the sign.
Pre-Algebra

13. Insert Lesson Title Here
13-4
Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 1C
Find the opposite of the polynomial.
A. 9a6b4 + a4b2 – 1
–(9a6b4 + a4b2 – 1)
–9a6b4 – a4b2 + 1
Distribute the sign.
Pre-Algebra

14. Subtracting Polynomials
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Subtracting Polynomials
To subtract a polynomial, add its opposite.
Pre-Algebra

15. Additional Example 2A: Subtracting Polynomials Horizontally
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Subtracting Polynomials
Additional Example 2A: Subtracting Polynomials Horizontally
Subtract.
A. (5x2 + 2x – 3) – (3x2 + 8x – 4)
Add the
opposite.
= (5x2 + 2x – 3) + (–3x2 – 8x + 4)
Associative
property.
= 5x2 + 2x – 3 – 3x2 – 8x + 4
= 2x2 – 6x + 1
Combine like
terms.
Pre-Algebra

16. Insert Lesson Title Here
13-4
Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 2A
Subtract.
A. (2y3 + 3y + 5) – (4y3 + 3y + 5)
Add the
opposite.
= (2y3 + 3y + 5) + (–4y3 – 3y – 5)
Associative
property.
= 2y3 + 3y + 5 – 4y3 – 3y – 5
= –2y3
Combine like
terms.
Pre-Algebra

17. Additional Example 2B: Subtracting Polynomials Horizontally
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Subtracting Polynomials
Additional Example 2B: Subtracting Polynomials Horizontally
Subtract.
B. (b2 + 4b – 1) – (7b2 – b – 1)
= (b2 + 4b – 1) + (–7b2 + b + 1)
Add the opposite.
Associative
property.
= b2 + 4b – 1 –7b2 + b + 1
= –6b2 + 5b
Combine like
terms.
Pre-Algebra

18. Insert Lesson Title Here
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Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 2B
Subtract.
B. (c3 + 2c2 + 3) – (4c3 – c2 – 1)
= (c3 + 2c2 + 3) + (–4c3 + c2 + 1)
Add the opposite.
= c3 + 2c2 + 3 – 4c3 + c2 + 1
Associative
property.
= –3c3 + 3c2 + 4
Combine like
terms.
Pre-Algebra

19. Subtracting Polynomials
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Subtracting Polynomials
You can also subtract polynomials in a vertical format. Write the second polynomial below the first one, lining up the decimal points.
Pre-Algebra

20. Additional Example 3A: Subtracting Polynomials Vertically
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Subtracting Polynomials
Additional Example 3A: Subtracting Polynomials Vertically
Subtract.
A. (2n2 – 4n + 9) – (6n2 – 7n + 5)
(2n2 – 4n + 9)
2n2 – 4n + 9
– (6n2 – 7n + 5)
+ –6n2 + 7n – 5
Add the
opposite.
–4n2 + 3n + 4
Pre-Algebra

21. Insert Lesson Title Here
13-4
Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 3A
Subtract.
A. (4r3 + 4r + 6) – (6r3 + 3r + 3)
(4r3 + 4r + 6)
4r3 + 4r + 6
– (6r3 + 3r + 3)
+ –6r3 – 3r – 3
Add the
opposite.
–2r3 + r + 3
Pre-Algebra

22. Additional Example 3B: Subtracting Polynomials Vertically
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Subtracting Polynomials
Additional Example 3B: Subtracting Polynomials Vertically
Subtract.
B. (10x2 + 2x – 7) – (x2 + 5x + 1)
(10x2 + 2x – 7)
10x2 + 2x – 7
– (x2 + 5x + 1)
+ –x2 – 5x – 1
Add the
opposite.
9x2 – 3x – 8
Pre-Algebra

23. Insert Lesson Title Here
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Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 3B
Subtract.
B. (13y2 – 2x + 5) – (y2 + 5x – 9)
(13y2 – 2x + 5)
13y2 – 2x + 5
– (y2 + 5x – 9)
+ –y2 – 5x + 9
Add the
opposite.
12x2 – 7x + 14
Pre-Algebra

24. Additional Example 3C: Subtracting Polynomials Vertically
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Subtracting Polynomials
Additional Example 3C: Subtracting Polynomials Vertically
Subtract.
C. (6a4 – 3a2 – 8) – (–2a4 + 7)
(6a4 – 3a2 – 8)
6a4 – 3a2 – 8
– (–2a4 + 7)
+ 2a – 7
Add the
opposite.
8a4 – 3a2 – 15
Pre-Algebra

25. Insert Lesson Title Here
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Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 3C
Subtract.
C. (5x2 + 2x + 5) – (–3x2 – 7x)
(5x2 + 2x + 5)
5x2 + 2x + 5
– (–3x2 – 7x)
+3x2 + 7x
Add the
opposite.
8x2 + 9x + 5
Pre-Algebra

26. Additional Example 4: Business Application
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Subtracting Polynomials
Additional Example 4: Business Application
Suppose the cost in dollars of producing x bookcases is given by the polynomial x, and the revenue generated from sales is given by the polynomial 216x – 75. Find a polynomial expression for the profit from producing and selling x bookcases, and evaluate the expression for x = 95.
216x – 75 – ( x)
revenue – cost
216x – 75 + (–250 – 128x)
Add the opposite.
216x – 75 – 250 – 128x
Associative Property
Combine like terms.
88x – 325
Pre-Algebra

27. Additional Example 4 Continued
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Subtracting Polynomials
Additional Example 4 Continued
The profit is given by the polynomial 88x – 325.
For x = 95,
88(95) – 325 = 8360 – 325 = 8035
The profit is $8035.
Pre-Algebra

28. Insert Lesson Title Here
13-4
Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 4
Suppose the cost in dollars of producing x baseball bats is given by the polynomial x, and the revenue generated from sales is given by the polynomial 35x – 5. Find a polynomial expression for the profit from producing and selling x baseball bats, and evaluate the expression for x = 50.
35x – 5 – (6 + 12x)
revenue – cost
35x – 5 + (–6 – 12x)
Add the opposite.
35x – 5 – 6 – 12x
Associative Property
23x – 11
Combine like terms.
Pre-Algebra

29. Subtracting Polynomials Insert Lesson Title Here
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Subtracting Polynomials
Insert Lesson Title Here
Try This: Example 4 Continued
The profit is given by the polynomial 23x – 11.
For x = 50,
23(50) – 11 = 1150 – 11 = 1139
The profit is $1139.
Pre-Algebra

30. Subtracting Polynomials Insert Lesson Title Here
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Subtracting Polynomials
Insert Lesson Title Here
Lesson Quiz
Find the opposite of each polynomial.
Subtract.
3. (3z2 – 7z + 6) – (2z2 + z – 12)
1. 3a2b2c3
–3a2b2c3
2. –3m3 + 2m2n
3m3 – 2m2n
z2 – 8z + 18
4. –18h3 – (4h3 + h2 – 12h + 2)
5. (3b2c + 5bc2 – 8b2)
– (4b2c + 2bc2 – c2)
– 22h3 – h2 + 12h – 2
– b2c + 3bc2 – 8b2 + c2
Pre-Algebra