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)


26