Slideshow 14 Mr Richard Sasaki Adding and Subtracting Polynomials – Part 2 Slideshow 14 Mr Richard Sasaki

Objectives Review how to add polynomials by removing brackets Learn how to add polynomials in vertical form Learn how to subtract polynomials in vertical form

Adding Polynomials How do each of these expand? (𝑎𝑥+𝑏𝑦)+(𝑐𝑥−𝑑𝑦)= 𝑎𝑥+𝑏𝑦+𝑐𝑥−𝑑𝑦 (𝑎𝑥+𝑏𝑦)−(𝑐𝑥−𝑑𝑦)= 𝑎𝑥+𝑏𝑦−𝑐𝑥+𝑑𝑦 −(𝑎𝑥+𝑏𝑦)+(𝑐𝑥−𝑑𝑦)= −𝑎𝑥−𝑏𝑦+𝑐𝑥−𝑑𝑦 −(𝑎𝑥+𝑏𝑦)−(𝑐𝑥−𝑑𝑦) = −𝑎𝑥−𝑏𝑦−𝑐𝑥+𝑑𝑦 Today we will learn how to complete challenging questions like… 14 12 2 6 Calculate 14+12 in vertical form. Congratulations.

Adding Polynomials 14𝑥+7𝑦 10𝑥+3𝑦 24𝑥 +10𝑦 You can add polynomials in the same way. It doesn’t matter whether you calculate from the left first or from the right first. As it’s more natural, let’s go from the left. 14𝑥+7𝑦 10𝑥+3𝑦 Not very difficult was it? 24𝑥 +10𝑦 The style of calculating vertically makes things easier but it takes longer.

Adding Polynomials (3𝑦+2𝑧−4)+(7𝑥 –9𝑦+3) 3𝑦+2𝑧 −4 7𝑥−9𝑦 +3 7𝑥 + 2𝑧 − 1 This can also be done with different terms in each expression and more than two. (3𝑦+2𝑧−4)+(7𝑥 –9𝑦+3) 3𝑦+2𝑧 −4 Make sure the terms are aligned together. 7𝑥−9𝑦 +3 7𝑥 − 6𝑦 + 2𝑧 − 1 Places with spaces of course imply 0. We must be careful when we subtract.

Subtracting Polynomials We can also subtract polynomials like this. Place the first one at the top and the second one at the bottom. Again, we can calculate from the left or right, it doesn’t matter. 14𝑥+7𝑦 10𝑥+3𝑦 Not very difficult was it? 4𝑥 + 4𝑦

Subtracting Polynomials With more complicated problems, we must consider positive and negative numbers carefully. 3𝑦+2𝑧−4 −(7𝑥 –9𝑦+3) 0𝑥+ 3𝑦+2𝑧 −4 7𝑥−9𝑦 +3 −7𝑥 +12𝑦 + 2𝑧 −7 Zeroes are important, especially in the first polynomial.

7𝑥+8𝑦 15𝑥+9𝑦 𝑥−2𝑦 4𝑥+𝑦 6𝑥+8𝑦 9𝑥+𝑦 15𝑥+9𝑦 7𝑥+3𝑦 − 4𝑥+2𝑦 3𝑥+ 𝑦 7𝑥+4𝑦 3𝑥−12 −𝑦+20 7𝑥+12𝑦+9 2𝑥+2𝑦+2𝑧 − 𝑥+ 𝑦+ 𝑧 𝑥+ 𝑦+ 𝑧 6𝑥+3𝑦+2𝑧−4 + 6𝑥+3𝑦+2𝑧−4 12𝑥+6𝑦+4𝑧−8

3𝑥+2𝑦 +(5𝑥+8𝑦) 3𝑥+ 2𝑦 + 5𝑥+ 8𝑦 8𝑥+10𝑦 8 10 3𝑦+ 2𝑧 − 𝑦− 5𝑧 2𝑦+7𝑧 4𝑥+3𝑦−10 + 2𝑥+5𝑦 11𝑥+2𝑦+2𝑧+5 6𝑥+8𝑦−10 5𝑦 5𝑦 5𝑥 𝑦 −5𝑥 4𝑥 3𝑦 12𝑥

3 𝑦 2 +𝑥𝑦 −3 + 9 𝑦 2 −𝑥𝑦+4𝑥−2 12 𝑦 2 +4𝑥−5 −𝑦−4 3𝑥+3𝑦 −2 5𝑥−8𝑦 +3 + _ 𝑦+𝑧 ___ __ 8𝑥−4𝑦+𝑧 +1 3 𝑥 2 +3 𝑦 2 −𝑧 + 3 𝑥 2 +3 𝑦 2 −𝑧 𝑥−1 6 𝑥 2 +6 𝑦 2 −2𝑧 −12 𝑥 2 +4 𝑥 3 −8𝑥+14 3𝑥+2𝑦 2 cows.