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A-
A
A+
Factorise
(i) 25x
2
- 36y
2
(ii) 2ab - a
2
- b
2
+ 1
(iii) 36a
2
- 12a + 1 - 25b
2
(iv) a
4
- 81b
4
(v) a
12
b
4
- a
4
b
12
(vi) 4x
2
- 9y
2
- 2x - 3y
(i) 25x
2
- 36y
2
= (5x)
2
- (6y)
2
= (5x + 6y) (5x - 6y)
(ii) 2ab - a
2
- b
2
+ 1
= 1 - (a
2
+ b
2
- 2ab)
= 1 - (a - b)
2
= (1 + a - b) (1 - a + b)
(iii) 36a
2
- 12a + 1 - 25b
2
= (6a)
2
- 2 x 6a x 1 + 1
2
- (5b)
2
= (6a - 1)
2
- (5b)
2
= (6a - 1 + 5b) (6a - 1 - 5b)
= (6a + 5b - 1) (6a - 5b - 1)
(iv) a
4
- 81b
4
= (a
2
)
2
- (9b
2
)
2
= (a
2
+ 9b
2
) (a
2
- 9b
2
)
= (a
2
+ 9b
2
) (a + 3b) (a - 3b)
(v) a
12
b
4
- a
4
b
12
= a
4
b
4
(a
8
- b
8
)
= a
4
b
4
[(a
4
)
2
- (b
4
)
2
]
= a
4
b
4
(a
4
+ b
4
) (a
4
- b
4
)
= a
4
b
4
(a
4
+ b
4
) (a
2
+ b
2
) (a
2
- b
2
)
= a
4
b
4
(a
4
+ b
4
) (a
2
+ b
2
) (a + b) (a - b)
(vi) 4x
2
- 9y
2
- 2x - 3y
= (2x)
2
- (3y)
2
- (2x + 3y)
= (2x + 3y) (2x - 3y) - (2x + 3y)
= (2x + 3y) (2x - 3y - 1)
12
