# Expanding and factorising

> Grade 8: expand a single bracket, factorise by taking out a common factor, collect like terms after expanding, substitute into a formula, rearrange a simple formula.

Source: https://olyclass.com/library/math-g8-expand-factorise-en/

- Subject: Math
- Level: Grade 8
- Practice: 16
- Play it free on one screen (projector, TV or whiteboard): https://olyclass.com/library?play=math-g8-expand-factorise-en
- Copy and edit it: https://olyclass.com/library?copy=math-g8-expand-factorise-en
- Games it plays well in: [Ring the Bell](https://olyclass.com/classroom-games/ring-the-bell/), [High Water](https://olyclass.com/classroom-games/high-water/), [Tug of War](https://olyclass.com/classroom-games/tug-of-war/), [Lucky Wheel](https://olyclass.com/classroom-games/lucky-wheel/)

## Questions

1. Expand 3(x + 4) (3x + 12 / 3x + 4 / 3x + 7 / x + 12)
   Answer: 3x + 12
2. Expand 5(2a − 3) (10a + 15 / 10a − 15 / 10a − 3 / 7a − 15)
   Answer: 10a − 15
3. Expanding 4(y + 2) gives 4y + 8.
   Answer: True
4. Factorise 6x + 9 by taking out the highest common factor. (2(3x + 9) / 3(2x + 3) / 3(2x + 9) / 6(x + 9))
   Answer: 3(2x + 3)
5. Factorise 8a − 12 (2(4a − 3) / 4(2a − 12) / 4(2a − 3) / 8(a − 12))
   Answer: 4(2a − 3)
6. What is the highest common factor of 12x and 18?
   Answer: 6
7. Expand and simplify 2(x + 3) + 4x (2x + 18 / 6x + 3 / 6x + 6 / 8x + 6)
   Answer: 6x + 6
8. Expand and simplify 3(x + 2) + 2(x − 1) (5x + 4 / 5x + 5 / 5x + 8 / 5x − 4)
   Answer: 5x + 4
9. Factorising 5x² + 10x gives 5x(x + 2).
   Answer: True
10. Expand and simplify 4(x + 5) − 2x.
   Answer: 2x + 20
11. Using P = 2l + 2w, find P when l = 7 and w = 3. (13 / 17 / 20 / 21)
   Answer: 20
12. Using v = u + 5t, find v when u = 4 and t = 3. (12 / 15 / 19 / 27)
   Answer: 19
13. If y = 3x − 2 and x = 4, then y = 14.
   Answer: False
14. Rearrange y = x + 7 to make x the subject. (x = 7 − y / x = 7y / x = y + 7 / x = y − 7)
   Answer: x = y − 7
15. Make x the subject of y = 3x. (x = 3 − y / x = 3y / x = y ÷ 3 / x = y − 3)
   Answer: x = y ÷ 3
16. Make x the subject of y = 2x + 5.
   Answer: x = (y − 5) ÷ 2