Name: Date: Period: Topic: Adding & Subtracting Polynomials Essential Question : How can you use monomials to form other large expressions? Warm – Up:

Name:Date:Period:Topic: Adding & Subtracting PolynomialsEssential Question: How can you use monomials to form other large expressions?

Warm – Up:Write an equation of the line that passes

through the given point and is perpendicular to the graph of the given equation.

(3, 2); - 3x + y = - 2

Copy down the following expressions and circle the like

terms. 1. 7x2 + 8x -2y + 8 – 6x

2. 3x – 2y + 4x2 – y

3. 6y + y2 – 3 + 2y2 – 4y3

Flashback!!! Do you remember what like terms are???

Adding & Subtracting Polynomials Vocabulary:

Monomial – is a real number, a variable, or a product of a real number and one or more variables with whole-number exponents. Ex: x, p, 4xy, 6, - 2r

Degree of Monomial – is the sum of the exponents of its variables. Ex: 34p2q3r = Degree of the monomial = 6

Polynomial – is a monomial or a sum of monomials. Ex: 4x2 + 7x + 3 – 2y – 5xy

Degree of a Polynomial - based on the degree of the monomial with the greatest exponent. Ex: 4x2 + 7x + 3 Degree of the polynomial = 2

Solve the polynomials.

1. x2 + 3x + 7y + xy + 8

2. x2 + 4y + 2x + 3

3. 3x + 7y + 8

4. x2 + 11xy + 8

x2 + 4y + 3 + 2x and 3y + 5 + xy + x

Find the sum. Write the answer in standard format.

(5x 3 – x + 2 x 2 + 7) + (3x 2 + 7 – 4 x) + (4x 2 – 8 – x 3)

Adding Polynomials

SOLUTION

Vertical format: Write each expression in standard form. Align like terms.

5x 3 + 2 x 2 – x + 7

3x 2 – 4 x + 7

– x 3 + 4x 2 – 8+

4x 3 + 9x 2 – 5x + 6

Find the sum. Write the answer in standard format.

(2 x 2 + x – 5) + (x + x 2 + 6)

Adding Polynomials

SOLUTION

Horizontal format: Add like terms.

(2 x 2 + x – 5) + (x + x 2 + 6) = (2 x 2 + x 2) + (x + x) + (–5 + 6)

= 3x 2 + 2 x + 1

1. (9y - 7x + 15a) + (- 8a + 8x -3y )

2. (3a2 + 3ab - b2) + (4ab + 6b2)

3. (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)

Add the following polynomials:

Practice Time!

4. Find the sum.(5a – 3b) + (6b + 2a)

a) 3a – 9b

b) 3a + 3b

c) 7a + 3b

d) 7a – 3bPractice Time!

Find the difference.

(–2 x 3 + 5x

2 – x + 8) – (–4 x 3 + 3x – 4)

Subtracting Polynomials

SOLUTION

Use a vertical format. To subtract, you add the opposite. This means you multiply each term in the subtracted polynomial by –1 and add.

–2 x 3 + 5x 2 – x + 8

–4 x 3 + 3x – 4– Add the opposite

No change –2 x 3 + 5x 2 – x + 8

4 x 3 – 3x + 4+

Find the difference.

(–2 x 3 + 5x 2 – x + 8) – (–4 x 2 + 3x – 4)

Subtracting Polynomials

SOLUTION

Use a vertical format. To subtract, you add the opposite. This means you multiply each term in the subtracted polynomial by –1 and add.

–2 x 3 + 5x 2 – x + 8

–4 x 3 + 3x – 4–

2x 3 + 5x 2 – 4x + 12

–2 x 3 + 5x 2 – x + 8

4 x 3 – 3x + 4+

Find the difference.

(3x 2 – 5x + 3) – (2 x 2 – x – 4)

Subtracting Polynomials

SOLUTION

Use a horizontal format.

(3x 2 – 5x + 3) – (2 x 2 – x – 4)

= x 2 – 4x + 7

= (3x 2 – 5x + 3) + (– 2 x 2 + x + 4)

= (3x 2 – 2 x 2) + (– 5x + x) + (3 + 4)

4. (15a + 9y - 7x) - (-3y + 8x - 8a)

5. (7a - 10b) - (3a + 4b)

6. (4x2 + 3y2 - 2xy) - (2y2 - xy - 3x2)

Subtract the following polynomials:

Practice Time!

Find the difference.(5a – 3b) – (2a + 6b)

a) 3a – 9b

b) 3a + 3b

c) 7a + 3b

d) 7a – 9bPractice Time!

Additional Practice:

Page 477 (1 - 4) Page 478 (30, 32, 36, 43)

Home-Learning #1:

Page 478 (38, 40, 43, 46, 53)