8.2 Add and Subtract Polynomials ink.notebook

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8.2 Add and Subtract Polynomials

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Lesson Objectives Standards Lesson Notes

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8.2 Adding and Subtracting Polynomials

Lesson Objectives

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Lesson NotesStandards

A.SSE.2 I will rewrite a polynomial into standard form A.APR.1 I will simplify polynomial expressions adding and subtracting like terms

8.2 Add and Subtract Polynomials ink.notebook

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Lesson Objectives Standards

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Lesson Notes

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Add Polynomials To add polynomials, you can group like terms horizontally or write them in column form, aligning like terms vertically. Like terms are monomial terms that are either identical or differ only in their coefficients, such as 3p and −5p or 2x2y and 8x2y.

Adding Polynomials (Combine like terms)

Do NOT change the exponents on the variables

*Be careful of negative signs*

(3x2 + 4x) + (-6x2 + x)

(5x2 - 8) + (2x2 - 3x + 1)

a)

b)

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Subtracting PolynomialsChange subtract to add and change the sign on EVERY term in the SECOND polynomial.

Then follow the rules of adding

(3x2 + 4x) - (-6x2 + x)

(5x2 - 8) - (2x2 - 3x + 1)

(3x2 + 4x) + (6x2 - x)becomes

now combine like terms:

becomes

now combine like terms:

c)

d)

Find each sum or difference.1. (x2 + y2) + (−x2 + y2)

2. (2a − 8b) − (−3a + 5b)

3. (2x2 − 6) + (5x2 + 2) + (−x2 − 7)

Find each sum or difference.

4. (2x2 − 8) − (−2x2 − 6)

5. (9xy2 + 5xy) − (−2xy − 8xy2)

6. (x2 − 6x + 2) − (−5x2 + 7x − 4)

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Find each sum or difference.

8. (6xy2 + 4xy) + (2xy − 10xy2 + y2)

7. (2p − 5r) + (3p + 6r) + (p − r)

9. The measures of two sides of a triangle are given. If P is the perimeter, and P = 10x + 5y, find the measure of the third side.

3x + 4y

5x ­ y

10. The polynomial s3 − 70s2 + 1500s − 10,800 models the profit a company makes on selling an item at a price s. A second item sold at the same price brings in a profit of s3 − 30s2 + 450s − 5000. Write a polynomial that expresses the total profit from the sale of both items.

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On Your Whiteboards

(3a − 5) − (5a + 1)

(9x + 2) − (−3x2 − 5)

(9xy + y − 2x) − (6xy − 2x)

Find each sum or difference.a)

b)

c)

Find each sum or difference.

(6x2 − 5x + 1) − (−7x2 − 2x + 4)

(2m2 + 5m + 1) − (4m2 − 3m − 3)

(2x2 − 6x − 2) + (x2 + 4x) + (3x2 + x + 5) d)

e)

f)

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On the Worksheet Homework

Find each sum or difference.

1. (6x3 – 4) + (–2x3 + 9)

2. (g3 – 2g2 + 5g) – (g2 + 2g)

3. (4 + 2a2 – 2a) – (3a2 – 8a + 7)

4. (8y – 4y2) + (3y – 9y2)

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5. (–4z3 – 2z2 + 8) – (4z3 + 3z2 – 5)

6. (–3d2 – 8 + 2d) + (4d – 12 + d2)

7. (2c2 + 6c + 4) + (5c2 – 7)

8. (3n3 – 5n + n2) – (–8n2 + 3n3)

9. (y + 5) + (2y + 4y2 – 2)

10. (3c2 – c + 11) – (c2 + 2c + 8)

11. Write the polynomial that represents the perimeter of the figure at the right.

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12. Kim is painting two walls of her bedroom. The area of one wall can be modeled by 3x2 + 14 and the area of the other wall can be modeled by 2x – 3. What is the total area?

Express the perimeter of each figure as a polynomial in simplest form.

3x-1

3x-1

3x-1

3x-113. 14.

5y-3

4y

6y-1

4y+2

Simplify each.

15. t(t5)(t7) 16. (5t5v2)(10t3v4)

Simplify each.

17. 18.

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19. The total number of students T who traveled for spring break consists of two groups: students who flew to their destinations F and students who drove to their destination D. The number (in thousands) of students who flew and the total number of students who flew or drove can be modeled by the following equations, where n is the number of years since 1995.

T = 14n + 21 F = 8n + 7

Write an equation that models the number of student who drove to their destination for this time period.

20. From 1997 through 2007, the number of dogs D and the number of cats C (in hundreds) adopted from animal shelters in the United States are modeled by the following equations, where n is the number of years since 1997.

D = 2n + 3 C = n + 4

Write an equation that models the total number T of dogs and cats adopted in hundreds for this time period.

21. The width of a rectangle is represented by 5x + 2y, and the length is represented by 6y – 2x. Write a polynomial that represents the perimeter.

22. The perimeter of the figure at the right is represented by the expression 3x2 – 7x + 2. Write a polynomial that represents the measure of the third side

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23. Which ordered pair is in the solution set of the system of inequalities shown in the graph?

a) (–3, 0) b) (0, –3)

c) (5, 0) d) (0, 5)

Answers: