This document provides guidance on how to add and subtract polynomials by working through examples of adding and subtracting terms with variables like x, y, and a. It shows how to group like terms, write polynomials in column form, and change subtraction to addition of the opposite term in order to combine polynomials. The examples calculate the sum or difference of polynomials like (4x^2 - 2xy + 3y^2) + (-3x^2 - xy + 2y^2).

1. Guiding Question How do we add and subtract polynomials? Entry point : I have two baskets of fruit. In one basket, I have 3 apples, 5 bananas, and 7 cupcakes. In another basket I have 6 apples, 8 bananas and 2 cupcakes. How many apples, bananas and cupcakes do I have?

2. 1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. 9y - 3y - 7x + 8x + 15a - 8a 6y + x + 7a

3. Combine your like terms. 3a 2 + 3ab + 4ab - b 2 + 6b 2 3a 2 + 7ab + 5b 2 2. Add the following polynomials: (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 )

4. Add the polynomials. + x 2 + 3x + 7y + xy + 8 x 2 + 4y + 2x + 3 3x + 7y + 8 x 2 + 11xy + 8 X 2 1 1 X X XY Y Y Y Y 1 1 1 X Y Y Y 1 1 1

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

6. 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: (9y - 7x + 15a) - (-3y + 8x - 8a)

7. Rewrite subtraction as adding the opposite. (7a - 10b) + ( - 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b)

8. Line up your like terms and add the opposite. 4x 2 - 2xy + 3y 2 + ( + 3x 2 + xy - 2y 2 ) -------------------------------------- 7x 2 - xy + y 2 6. Subtract the following polynomials using column form: (4x 2 - 2xy + 3y 2 ) - (-3x 2 - xy + 2y 2 )

9. Find the sum or difference. (5a – 3b) + (2a + 6b) 3a – 9b 3a + 3b 7a + 3b 7a – 3b

10. Find the sum or difference. (5a – 3b) – (2a + 6b) 3a – 9b 3a + 3b 7a + 3b 7a – 9b