Question

What do we get after factorising x^3+ 8y^3+ z^3 – 4xyz?

(a) (x + 2y + z) (x^2 + 4y^2 + z^2 – 2xy – 2yz – zx)

(b) (x + 2y + z) (x^2 + 4y^2 + z^2 – 2xy – 2yz – zx)

(c) (x + 2y + z) (x^2 + 4y^2 + z^2 – 2xy – 2yz – zx)

(d) (x + 2y + z) (x^2 + 4y^2+  z^2 – 2xy – 2yz – zx)

I have been asked this question by my college director while I was bunking the class.

This intriguing question originated from Factorisation of Polynomials and Algebraic Identities in division Polynomials of Mathematics – Class 9

Answer 1

Correct answer is (c) (x + 2y + z) (x^2 + 4y^2 + z^2 – 2xy – 2yz – zx)

Explanation: We know that a^3 + b^3 + c^3 – 3abc = (a+b-c)(a^2 + b^2 + c^2 – ab – bc – ca)

In x^3 + 8y^3 + y^3 – 6xyz, a=x, b=2y and c=z

By using the above equation, we get x^3 + 8y^3 + z^3 – 4xyz = (x+2y+z) (x^2 + (2y)^2 + z^2 – x(2y) – (2y)(z) – zx)

= (x + 2y + z) (x^2 + 4y^2 + z^2 – 2xy – 2yz – zx).