Mathematics
Factorise the following:
64x6 - 729y6
Factorisation
45 Likes
Answer
64x6 - 729y6 = [(2x)3]2 - [(3y)3]2.
We know that,
a2 - b2 = (a + b)(a - b).
∴ [(2x)3]2 - [(3y)3]2 = [{(2x)3 - (3y)3}{(2x)3 + (3y)3}]
We know that,
a3 - b3 = (a - b)(a2 + ab + b2).
a3 + b3 = (a + b)(a2 - ab + b2).
∴ [{(2x)3 - (3y)3}{(2x)3 + (3y)3}] = (2x - 3y)[(2x)2 + 2x.3y + (3y)2](2x + 3y)[(2x)2 - 2x.3y + (3y)2]
= (2x - 3y)(4x2 + 6xy + 9y2)(2x + 3y)(4x2 - 6xy + 9y2)
Hence, 64x6 - 729y6 = (2x - 3y)(2x + 3y)(4x2 + 6xy + 9y2)(4x2 - 6xy + 9y2).
Answered By
24 Likes