Question

Factorise:- (a+2b)^3 + (2a-c)^3 - (a+2c)^3 + 3(a+2b)(2a-c)(a+2c).

Answer 1

Answer:

(a+2b)3+(2a -c)3+[- (a+2c)3] - 3(a+2b) (2a-c) (a+2c)

As,we know that,

x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)

Here,

x =  (a+2b),  y=(2a -c), z= - (a+2c)

Therefore,  

(a+2b)3+(2a -c)3+[- (a+2c)3]+3(a+2b) (2a-c) (a+2c)