Factorise the following:
11. 2ax - 3ay + 4bx - 6by
211
EXERCISE 14.2
1 x - xy + x - y
4. 3 xy + 7x - 77 - 372
2. a2 + ab + bc + ac
3. xy - 3y + x² – 3x
5. xy - xy2 + 5xy - 5y2
6. x3 + 3x2 + 2x + 6
8. x2 + 6y - xy - 6x
9. 2x2 – x(4a - 2b)-4ab
11. x(x + y - z) - yz
12. x²y + (y - 1)x - 1
14. (ax + by)2 + (bx - ay)2
15. (a2 + b2)xy - ab(x2 + y2)
17. x?yz + xy-z(z + 3y) - xyz-(x - 2y)
110.
z + x(5 + y) + 5y
13. 2yz - x(x - 2y +z)
Op?p3 + 27x?y3 – 36r3y2
Answers
Answer:
Factorisation
Exercise 14.2
Question 1: Find the common factors of the given terms.
(i) 12x, 36
Answer:
12
x
=
2
×
2
×
3
×
x
12x=2×2×3×x
36
=
2
×
2
×
3
×
3
36=2×2×3×3
Here, common factor
=
2
×
3
=
6
=2×3=6
(ii) 2y, 22xy
Answer:
2
y
=
2
×
y
2y=2×y
22
y
=
2
×
11
×
y
22y=2×11×y
Common factor = 2
(iii) 14 pq, 28 p2q2
Answer:
14
p
q
=
2
×
7
×
p
×
q
14pq=2×7×p×q
28
p
2
q
2
=
2
×
2
×
7
×
p
×
p
×
q
×
q
28p2q2=2×2×7×p×p×q×q
Common factor
=
2
×
7
×
p
×
q
=2×7×p×q
(iv) 2x, 3x², 4
Answer:
2
x
=
2
×
x
2x=2×x
3
x
2
=
3
×
x
×
x
3x2=3×x×x
4
=
2
×
2
4=2×2
Common factor = 1
There is no common factor other than unity, so common factor= 1
(v) 6 abc, 24ab², 12 a²b
Answer:
6
a
b
c
=
2
×
3
×
a
×
b
×
c
6abc=2×3×a×b×c
24
a
b
2
=
2
×
2
×
2
×
3
×
a
×
b
×
b
24ab2=2×2×2×3×a×b×b
12
a
2
b
=
2
×
2
×
3
×
a
×
a
×
b
12a2b=2×2×3×a×a×b
(vi) 16 x³, – 4x², 32x
Answer:
16
x
3
=
2
×
2
×
2
×
2
×
a
×
a
×
a
16x3=2×2×2×2×a×a×a
−
4
x
2
=
−
2
×
2
×
x
×
x
-4x2=-2×2×x×x
32
x
=
2
×
2
×
2
×
2
×
2
×
x
32x=2×2×2×2×2×x
Common factor
=
2
x
=2x
(vii) 10 pq, 20qr, 30rp
Answer:
10
p
q
=
2
×
5
×
p
×
q
10pq=2×5×p×q
20
q
r
=
2
×
2
×
4
×
q
×
r
20qr=2×2×4×q×r
30
r
p
=
2
×
3
×
5
×
r
×
p
30rp=2×3×5×r×p
Common factor
=
2
×
5
=
10
=2×5=10
(viii) 3x² y³, 10x³ y²,6 x² y²z
Answer:
3
x
2
y
3
=
3
×
x
×
x
×
y
×
y
×
y
3x2y3=3×x×x×y×y×y
10
x
3
y
2
=
2
×
5
×
x
×
x
×
x
×
y
×
y
10x3y2=2×5×x×x×x×y×y
x
2
y
2
z
=
x
×
x
×
y
×
y
×
z
x2y2z=x×x×y×y×z
Common factor
=
x
2
y
2
=x2y2
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