Question

Factorise :
(i) x^3 - (y+z)^3

Answer 1

Step-by-step explanation:

x3+y3+z3−3xyz=0

⇒x3+y3+3x2y+3xy2+z3−3xyz−3x2y−3xy2=0

⇒(x+y)3+z3−3xy(x+y+z)=0

⇒(x+y+z)((x+y)2+z2−(x+y)z)−3xy(x+y+z)=0

⇒(x+y+z)(x2+2xy+y2+z2−xy−xz−3xy)=0

⇒(x+y+z)(x2+y2+z2−xy−yz−zx)=0.