Factories:
i. 9x3 – 6x2 + 12x
ii. 8x3 – 72xy + 12x
iii. 18a3b3-27a2b3+36a3b2
(i) Let’s find out the HCF of 9x3 , 6x2 , 12x
3x | 9x3 , 6x2 , 12x |
3x2 , 2x , 4 |
3x is the highest common factor which divides 9x3, 6x2 and 12x.
So,
9x3 – 6x2 + 12x = 3x(3x2 - 2x + 4)
(ii) Let’s find out the HCF of 8x3, 72xy and 12x
4x | 8x3, 72xy, 12x |
2x, 18y, 3 |
4x is the highest common factor which divides 8x3, 72xy and 12x.
So,
8x3 – 72xy + 12x = 4x(2x2 – 18y + 3)
(iii) Let’s find out the HCF of 18a3b3, 27a2b3, 36a3b2
9a2b2 | 18a3b3, 27a2b3, 36a3b2 |
2ab, 3b, 4a |
9a2b2 is the highest common factor which divides 18a3b3, 27a2b3, 36a3b2.
So,
18a3b3 – 27a2b3 + 36a3b2 = 9a2b2 (2ab - 3b + 4a)