Adding and Subtracting Polynomials – Part 2 Slideshow 3 Mr Richard Sasaki Room 307

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

How do these expand? (Don’t factorise!) Review How do these expand? (Don’t factorise!) = (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

Addition What is 14 + 12? Show your calculation in vertical form. That sounds difficult..! Ooh… 14 Congratulations. 12 2 6

Adding Polynomials 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 That was pretty easy too, right? 10𝑥 + 3𝑦 24𝑥 + 10𝑦

7𝑥 − 6𝑦 + 2𝑧 − 1 (3𝑦 + 2𝑧 − 4) + (7𝑥 – 9𝑦 + 3) 3𝑦 + 2𝑧 − 4 7𝑥 − 9𝑦 + 3 Adding Polynomials 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

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) 14𝑥 + 7𝑦 Wasn’t that beautiful. 10𝑥 + 3𝑦 4𝑥 + 4𝑦

SUBTRACTING Polynomials Remember for more complicated subtraction problems, we have to deal with combinations of positives and negatives. (3𝑦 + 2𝑧 − 4) − (7𝑥 – 9𝑦 + 3) 3𝑦 + 2𝑧 −4 Make sure the terms are aligned together. 7𝑥 − 9𝑦 + 3 −7𝑥 + 12𝑦 + 2𝑧 − 7

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

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

Answers 𝟏𝟐𝒚𝟐+𝟒𝒙−𝟓 −𝒚−𝟒 𝟖𝒙 – 𝟒𝒚 + 𝒛 + 𝟏 𝟑𝒙 + 𝟐𝒚 𝟔𝒙𝟐+𝟔𝒚𝟐−𝟐𝒛 2 cows. 𝒙 −𝟏 −𝟏𝟐𝒙𝟐+𝟒𝒙𝟑−𝟖𝒙+𝟏𝟒 𝟏𝟐𝒚𝟐+𝟒𝒙−𝟓 −𝒚−𝟒 𝟖𝒙 – 𝟒𝒚 + 𝒛 + 𝟏 𝟑𝒙 + 𝟐𝒚 𝟔𝒙𝟐+𝟔𝒚𝟐−𝟐𝒛 two 2 cows. 𝒙 −𝟏