Homework Solution: lesson 7.3 page 446 37) x(x+3)(x-1) 38) x(x-6)(x+5) 39) x(x-3)(x+1) 43) (𝑥 2 +4)(𝑥−3) 44) (𝑥 2 −1)(𝑥+3) 45) (𝑥 2 −5)(𝑥−2)

Homework Lesson 7.1_page 430 #39-46 ALL

Lesson 7.1 Adding and Subtracting Polynomials

Objectives The student will be able to: 1. add and subtract polynomials. SOL: A.2b Designed by Skip Tyler, Varina High School

Like Terms Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers. Which terms are like? 3a2b, 4ab2, 3ab, -5ab2 4ab2 and -5ab2 are like. Even though the others have the same variables, the exponents are not the same. 3a2b = 3aab, which is different from 4ab2 = 4abb.

Constants are like terms. Which terms are like? 2x, -3, 5b, 0 -3 and 0 are like. Which terms are like? 3x, 2x2, 4, x 3x and x are like. Which terms are like? 2wx, w, 3x, 4xw 2wx and 4xw are like.

1. Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2) Combine your like terms. 3a2 + 3ab + 4ab - b2 + 6b2 3a2 + 7ab + 5b2

2. Add the following polynomials using column form: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Line up your like terms. 4x2 - 2xy + 3y2 + -3x2 - xy + 2y2 _________________________ x2 - 3xy + 5y2

Adding Polynomials Some people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms! (x2 + 3x + 1) + (4x2 +5) (x2 + 3x + 1) + (4x2 +5) 5x2 + 3x + 6 add these polynomials: (2a2+3ab+4b2) + (7a2+ab+-2b2) (2a2 + 3ab + 4b2) + (7a2 + ab + -2b2) (2a2+3ab+4b2) + (7a2+ab+-2b2) 9a2 + 4ab + 2b2

Adding Polynomials Add the following polynomials; you may stack them if you prefer:

Subtracting Polynomials Subtract: (3x2 + 2x + 7) - (x2 + x + 4) Step 1: Change subtraction to addition (Keep-Change-Change.). (3x2 + 2x + 7) + (- x2 - x - 4) Step 2: Underline OR line up the like terms and add. (3x2 + 2x + 7) + (- x2 + - x + - 4) 2x2 + x + 3

Rewrite subtraction as adding the opposite. 3. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a) Rewrite subtraction as adding the opposite. (9y - 7x + 15a) + (+ 3y - 8x + 8a) Group the like terms. 9y + 3y - 7x - 8x + 15a + 8a 12y - 15x + 23a

4. Subtract the following polynomials: (7a - 10b) - (3a + 4b) Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b

Subtracting Polynomials Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add:

Write each sum or difference as a polynomial in standard form Write each sum or difference as a polynomial in standard form. Then classify the polynomial by degree and by number of terms. (𝑥 4 + 5𝑥 2 +𝑥)−( 2𝑥 3 +𝑥+𝑥 4 −4)

Simplify by finding the perimeter: 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter: x2 + x c2 + 1 6c + 3 A B 2x2 2x2 4c2 + 2c + 5 x2 + x A = 5c2 + 8c + 9 B = 6x2 + 2x

Simplify by finding the perimeter: 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 2d2 + d – 4 3x2 – 5 x D C 3d2 – 5d x2 + 7 3d2 – 5d d2 + 7 D = 9d2 – 9d + 3 C = 8x2 – 10x + 14

Simplify by finding the perimeter: 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 3x2 – 5x a3 + 2a a + 1 E F x2 + 3 2a3 + a + 3 E = 3a3 + 4a + 4 F = 8x2 – 10x + 6