1. Name: Date: Period: Topic: Adding & Subtracting Polynomials Essential 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

2. Copy down the following expressions and circle the like terms. 1. 7x 2 + 8x -2y + 8 – 6x 2. 3x – 2y + 4x 2 – y 3. 6y + y 2 – 3 + 2y 2 – 4y 3 Flashback!!! Do you remember what like terms are???

3. 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: 34p 2 q 3 r = Degree of the monomial = 6  Polynomial – is a monomial or a sum of monomials. Ex: 4x 2 + 7x + 3 – 2y – 5xy  Degree of a Polynomial - based on the degree of the monomial with the greatest exponent. Ex: 4x 2 + 7x + 3 Degree of the polynomial = 2

4. Solve the polynomials. 1. x 2 + 3x + 7y + xy + 8 2. x 2 + 4y + 2x + 3 3. 3x + 7y + 8 4. x 2 + 11xy + 8 x 2 + 4y + 3 + 2x and 3y + 5 + xy + x

5. 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

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

7. 1. (9y - 7x + 15a) + (- 8a + 8x -3y ) 2. (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 ) 3. (4x 2 - 2xy + 3y 2 ) + (-3x 2 - xy + 2y 2 ) Add the following polynomials: Practice Time!

8. 4. Find the sum. (5a – 3b) + (6b + 2a) a) 3a – 9b b) 3a + 3b c) 7a + 3b d) 7a – 3b Practice Time!

9. 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 +

10. 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 +

11. 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)

12. 4. (15a + 9y - 7x) - (-3y + 8x - 8a) 5. (7a - 10b) - (3a + 4b) 6. (4x 2 + 3y 2 - 2xy) - (2y 2 - xy - 3x 2 ) Subtract the following polynomials: Practice Time!

13. Find the difference. (5a – 3b) – (2a + 6b) a) 3a – 9b b) 3a + 3b c) 7a + 3b d) 7a – 9b Practice Time!

14. Additional Practice: Page 477 (1 - 4) Page 478 (30, 32, 36, 43)

15. Home-Learning #1: Page 478 (38, 40, 43, 46, 53)