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

2. 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

3. 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

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

5. 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

6. 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 7𝑥
− 6𝑦
+ 2𝑧
− 1

7. 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

8. 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
−7𝑥
+ 12𝑦
+ 2𝑧
− 7

9. 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

10. 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

11. 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