#### Transcript Adding & Subtracting Polynomails

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 Flashback!!! Do you remember what like terms are??? 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 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. Degree of the monomial = 6 Polynomial – is a monomial or a sum of Ex: 34p2q3r = 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. x2 + 4y + 3 + 2x and 3y + 5 + xy + x 1. 2. 3. 4. x2 + 3x + 7y + xy + 8 x2 + 4y + 2x + 3 3x + 7y + 8 x2 + 11xy + 8 Adding Polynomials 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) SOLUTION Vertical format: Write each expression in standard form. Align like terms. 5x 3 + 2 x 2 – x + 7 3x 2 – 4 x + 7 3 2 + – x + 4x –8 4x 3 + 9x 2 – 5x + 6 Adding Polynomials Find the sum. Write the answer in standard format. (2 x 2 + x – 5) + (x + x 2 + 6) 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 Add the following polynomials: 1. (9y - 7x + 15a) + (- 8a + 8x -3y ) 2. (3a2 + 3ab - b2) + (4ab + 6b2) 3. (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Practice Time! 4. Find the sum. (5a – 3b) + (6b + 2a) a) b) c) d) 3a – 9b 3a + 3b 7a + 3b 7a – 3b Subtracting Polynomials Find the difference. (–2 x 3 + 5x 2 – x + 8) – (–4 x 3 + 3x – 4) 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 No change Add the opposite –2 x 3 + 5x 2 – x + 8 + 4 x3 – 3x + 4 Subtracting Polynomials Find the difference. (–2 x 3 + 5x 2 – x + 8) – (–4 x 2 + 3x – 4) 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 –2 x 3 + 5x 2 – x + 8 + 4 x3 – 3x + 4 2x 3 + 5x 2 – 4x + 12 Subtracting Polynomials Find the difference. (3x 2 – 5x + 3) – (2 x 2 – x – 4) SOLUTION Use a horizontal format. (3x 2 – 5x + 3) – (2 x 2 – x – 4) = (3x 2 – 5x + 3) + (– 2 x 2 + x + 4) = (3x 2 – 2 x 2) + (– 5x + x) + (3 + 4) = x 2 – 4x + 7 Subtract the following polynomials: 4. (15a + 9y - 7x) - (-3y + 8x - 8a) 5. (7a - 10b) - (3a + 4b) 6. (4x2 + 3y2 - 2xy) - (2y2 - xy - 3x2) Find the difference. (5a – 3b) – (2a + 6b) a) b) c) d) 3a – 9b 3a + 3b 7a + 3b 7a – 9b Additional Practice: Page 477 (1 - 4) Page 478 (30, 32, 36, 43) Home-Learning #1: Page 478 (38, 40, 43, 46, 53)