Algebraic expressions · Ages 13–14

Taking out a common factor worksheet

Part of: Factorisation

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Algebraic expressions · Ages 13–14

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Name:Date:Score:／48

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

13.Factorise 30x²y − 48xy². Put the steps in order.
- A. 30x²y − 48xy² = 6xy(5x − 8y)
- B. 30x²y ÷ 6xy = 5x, 48xy² ÷ 6xy = 8y
- C. Common factor = 6xy
- D. The H.C.F. of 30 and 48 = 6
Write the letters in the right order
Working:
Answer:
14.Factorise 9(x − 2) − x(x − 2). What do you get?
- A. (x − 2)²(9 − x)
- B. (x − 2)(9 + x)
- C. (x − 2)(x − 9)
- D. (x − 2)(9 − x)
Choose the right answer
Working:
Answer:
15.Tsz-hin factorises x(y − 9) − 3(y − 9) as (y − 9)(x + 3). The answer is right.
True or false?
Working:
Answer:
16.A rectangle has area (18x² + 12x) cm² and width 6x cm. Its length is (x + ) cm.
Fill in each blank
Working:
Answer:
17.Take out a common factor to work it out: 67 × 39 + 67 × 61 =
Working:
Answer:
18.A rectangle's perimeter is (18x + 4) cm, so its length plus its width is (x + ) cm.
Fill in each blank
Working:
Answer:

Show the answers and working

Taking out a common factor worksheet: Answers and working

1. 6, 7
The H.C.F. of 12 and 14 is 2: 12x ÷ 2 = 6x and 14 ÷ 2 = 7.
2. 2, 2, 3
The coefficients' H.C.F. is 2 and x's lowest index is 2: the common factor is 2x². 4x³ ÷ 2x² = 2x and 6x² ÷ 2x² = 3.
3. 9, 2
Both terms have the bracket (y + 9): take the whole of it out, (y + 9)(x + 2).
4. 4, 1
32x² ÷ 8x = 4x and 8x ÷ 8x = 1: taking out a whole term leaves 1 behind.
5. 5, 1
45x² ÷ 9x = 5x and 9x ÷ 9x = 1: taking out a whole term leaves 1 behind.
6. 5, 7, 6
The coefficients' H.C.F. is 5 and x's lowest index is 2: the common factor is 5x². 35x³ ÷ 5x² = 7x and 30x² ÷ 5x² = 6.
7. 9, 7
Both terms have the bracket (y + 9): take the whole of it out, (y + 9)(x + 7).
8. 9, 3, 2
The common factor is 2x; each term divided by it gives 9x², −3x and 2.

9. D. 6x(5x − 6)
The H.C.F. of 30 and 36 is 6, and both terms have x: the common factor is 6x. 30x² ÷ 6x = 5x and 36x ÷ 6x = 6.
10. C. 6x(6x − 1)
The H.C.F. of 36 and 6 is 6, and both terms have x: the common factor is 6x. 36x² ÷ 6x = 6x and 6x ÷ 6x = 1.
11. True
The common factor is 2xy, and every term inside is divided by it: 6x²y ÷ 2xy = 3x and 10xy² ÷ 2xy = 5y.
12. B. (x − 5)(2x − 5)
(x − 5) is common to both terms: 2x(x − 5) − 5(x − 5) = (x − 5)(2x − 5).

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

13. D → C → B → A
First the coefficients' H.C.F., then the letters every term has (x and y, each at least to index 1), then divide each term by the common factor.
14. D. (x − 2)(9 − x)
Both terms have (x − 2): 9(x − 2) − x(x − 2) = (x − 2)(9 − x).
15. False
With (y − 9) taken out, x and −3 stay in the other bracket: (y − 9)(x − 3).
16. 3, 2
Length = area ÷ width. 18x² + 12x = 6x(3x + 2), so the length is (3x + 2) cm.
17. 6700
67 × 39 + 67 × 61 = 67 × (39 + 61) = 67 × 100 = 6700.
18. 9, 2
Perimeter = 2 × (length + width). Take out the common factor 2: 18x + 4 = 2(9x + 2).

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