Algebraic expressions · Ages 13–14

Factorising by grouping worksheet

Part of: Factorisation

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Algebraic expressions · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

8.xy + 8x + 3y + 24 can be factorised as (x + 8)(y + 3).
True or false?
Answer:
9.Factorise xy − 4x − 2y + 8. What do you get?
- A. (x − 2)(y + 4)
- B. (x + 2)(y − 4)
- C. (x − 4)(y − 2)
- D. (x − 2)(y − 4)
Choose the right answer
Answer:
10.Factorise xy − 6x − 2y + 12. What do you get?
- A. (x − 2)(y + 6)
- B. (x − 6)(y − 2)
- C. (x + 2)(y − 6)
- D. (x − 2)(y − 6)
Choose the right answer
Answer:
11.xy + 5x + 7y + 35 can be factorised as (x + 5)(y + 7).
True or false?
Answer:
12.Factorise x³ + 6x² + 7x + 42. What do you get?
- A. (x − 6)(x² + 7)
- B. (x + 7)(x² + 6)
- C. (x + 6)(x² + 7)
- D. (x + 6)(x² − 7)
Choose the right answer
Answer:

13.x² + 7x − 5x − 35 = x(x + ) − 5(x + ) = (x + 7)(x − )
Fill in each blank
Working:
Answer:
14.Write xy + 7y + 2x + 14 as (xy + 7y) + (2x + 14). Once a factor is taken out of each pair, the brackets are exactly the same.
True or false?
Working:
Answer:
15.Group in pairs to work it out: 36 × 31 + 36 × 69 + 49 × 31 + 49 × 69 =
Working:
Answer:
16.A rectangular plot has area (xy + 8x + 6y + 48) m² and length (x + 6) m. Its width is (y + ) m.
Working:
Answer:
17.Factorise xy − 4x − 7y + 28. Put the steps in order.
- A. = (y − 4)(x − 7)
- B. = x(y − 4) − 7(y − 4)
- C. xy − 4x − 7y + 28 = (xy − 4x) − (7y − 28)
Write the letters in the right order
Working:
Answer:
18.Factorise 5x² − 25x + 6x − 30. What do you get?
- A. (x − 5)(5x + 6)
- B. (x + 5)(5x − 6)
- C. (x − 5)(5x − 6)
- D. (x − 6)(5x + 5)
Choose the right answer
Working:
Answer:

Show the answers and working

Factorising by grouping worksheet: Answers and working

1. 2, 3
In pairs: x(y + 3) + 2(y + 3) = (x + 2)(y + 3).
2. 2, 5
xy + 2x = x(y + 2) and 5y + 10 = 5(y + 2): the two brackets match.
3. 3, 6
In pairs: x(y + 6) + 3(y + 6) = (x + 3)(y + 6).
4. 3, 6
xy + 3x = x(y + 3) and 6y + 18 = 6(y + 3): the two brackets match.
5. 6, 1
x(y + (1)) + (6)(y + (1)) = (x + (6))(y + (1)): h = 6, k = 1.
6. 4
(6x + 6y) − (2x + 2y) = 6(x + y) − 2(x + y) = 4(x + y).
7. 2
(4x + 4y) − (2x + 2y) = 4(x + y) − 2(x + y) = 2(x + y).

8. False
xy + 8x + 3y + 24 = x(y + 8) + 3(y + 8) = (x + 3)(y + 8).
9. D. (x − 2)(y − 4)
xy − 4x − 2y + 8 = x(y − 4) − 2(y − 4) = (y − 4)(x − 2).
10. D. (x − 2)(y − 6)
xy − 6x − 2y + 12 = x(y − 6) − 2(y − 6) = (y − 6)(x − 2).
11. False
xy + 5x + 7y + 35 = x(y + 5) + 7(y + 5) = (x + 7)(y + 5).
12. C. (x + 6)(x² + 7)
x³ + 6x² + 7x + 42 = x²(x + 6) + 7(x + 6) = (x + 6)(x² + 7).

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 7, 7, 5
Take x out of the first pair, x(x + 7); −5 out of the second, −5(x + 7); then the shared (x + 7).
14. True
The first pair is y(x + 7); for the second to be 2(x + 7), its number must be 2 × 7 = 14.
15. 8500
= 36(31 + 69) + 49(31 + 69) = (36 + 49) × 100 = 85 × 100 = 8500.
16. 8
By grouping: xy + 8x + 6y + 48 = x(y + 8) + 6(y + 8) = (x + 6)(y + 8), so the width is (y + 8) m.
17. C → B → A
Pair the terms (a minus before the second pair changes the signs inside), take a factor out of each, then the shared bracket (y − 4).
18. A. (x − 5)(5x + 6)
5x² − 25x + 6x − 30 = 5x(x − 5) + 6(x − 5) = (x − 5)(5x + 6).

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