Factorize:
12(x2 + 7x)2 – 8(x2 + 7x) (2x – 1) – 15(2x – 1)2
Given, 12(x2 + 7x)2 – 8(x2 + 7x) (2x – 1) – 15(2x – 1)2
By splitting the middle term i.e. 8(x2 + 7x) (2x – 1), we get
= 12(x2 + 7x)2 – 18(x2 + 7x) (2x – 1) + 10(x2 + 7x) (2x – 1) – 15(2x – 1)2
= 6(x2 + 7x) [2(x2 + 7x) – 3(2x – 1)] + 5(2x - 1) [2(x2 + 7x) – 3(2x – 1)]
= [2(x2 + 7x) – 3(2x – 1)] [6(x2 + 7x) + 5(2x – 1)]
= (2x2 + 14x – 6x + 3) (6x2 + 42x + 10x – 5)
= (2x2 + 8x + 3) (6x2 + 52x - 5)