Question

Factorise : (x+1)power6- (x-1 )power 6

Answer 1

Solution:

(x+1)^6 - (x-1)^6

= [(x+1)³]² - [(x-1)³]²

= [(x+1)³+(x-1)³][(x+1)³-(x-1)³]

= (x+1+x-1)[(x+1)²-(x+1)(x-1)+(x-1)²][x+1-(x-1)][(x+1)²+(x+1)(x-1)+(x-1)²]

= (2x)[(x+1)²-(x²-y²)+(x-1)²]*2[(x+1)²+(x²-y²)+(x-1)²]

= 4x[2(x²+1²)-x²-y²][2(x²+1²)+x²-y²]

= 4x(2x²+2-x²-y²)(2x²+2+x²-y²)

=4x(x²-y²+2)(3x²-y²+2)

••••