Question

factorise (x-2y)^3 - (2y-3z)^3 + (3z-x)^3​

Answer 1

Question:factories (x-2y)^3 - (2y-3z)^3 + (3z-x)^3

a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)

If,

a+b+c=0

Then,

a^3+b^3+c^3=3abc

Here,

a=x-2y

b=2y-3z

c=3z-x

Thus,

(x-2y)+(2y-3z)+(3z-x)=0

And then,

(x-2y)^3+(2y-3z)^3+(3z-x)3^=3(x-2y)(2y-3z)(3z-x)

Hope it helps.