Adding and Subtracting Polynomials 1 Slideshow 13, Mr Richard Sasaki, Room 307

Objectives Review how to collect like terms [eg: 2x + x + 2y = ?] Understanding the impact of terms in brackets [eg: -(x + y) = ?] Being able to add polynomials [eg: (3x + 2y) + (-2x + 5y) = ?]

Review You have two minutes to complete the worksheet given.

Answers Please check your answers. 1)6x 2)6y 3)2x 4)-y 5)x 6)-x –y 7)x + 4 8)2x -3y 9)a – 3b 10)4y + x 11)0 12)2x - 6/y

- - + -(x + y - z) = -x - y + z What do brackets do? Something on the outside of a bracket will affect the terms in the bracket. - - + -(x + y - z) = -x - y + z

Removing Brackets If we can remove brackets from expressions, then we can simplify expressions with multiple brackets by collecting like terms. Expressions can also be referred to as polynomials (unless they go on forever). For example, 1 + x + x2 + … + x∞ is not a polynomial.

(3x+4y)+(2x-5y) = 3x+4y+2x-5y = 5x-y Example Simplify… Oh, no change! This is because both pairs of brackets have a + sign in front of them. = 5x-y Nice and easy!

(3x+4y)-(2x-5y) = 3x+4y-2x+5y = x+9y Example Simplify… Ahh… Because of the minus symbol in front of the second bracket, the operators swapped… = x+9y A little more confusing!

-(3x+4y)+(2x-5y) = -3x-4y+2x-5y = -x-9y Example Simplify… It doesn’t matter which bracket has a minus symbol, those terms’ + or – symbols will swap. = -x-9y

-(3x+4y)-(2x-5y) = -3x-4y-2x+5y = -5x+y Example Simplify… As both sets of brackets have a “-” in front of them, all + and – symbols have swapped. = -5x+y

5x-y x+9y -x-9y -5x+y Answers Doesn’t that seem strange? Look at the answers! 5x-y x+9y Doesn’t that seem strange? -x-9y -5x+y

Worksheet Please complete the questions on the worksheet provided.

Answers 5x+11y 4x+y 3x+y 2a + 2b 11x+18y + 10z 5z - 2y 8x - 2 5z - 2y 8x - 2 (10 + 3x) + (7 + 4x) 15x - 5 7x + 17 4x+6y 7x – 6y + 8 3x + 2 6a + 6b + 6c