Question

Factorise the polynomial x3 + 8y3 + 64 z3 – 24xyz​

Answer 1

Answer:

(x + 2y + 4z)(x^2 + 4y^2 + 16z^2 - 2xy - 8yz - 4xz)

Step-by-step explanation:

Given Equation = x^3 + 8y^3 + 64z^3 - 24xyz.

= (x)^3 + (2y)^3 + (4z)^3 - 3(x)(2y)(4z)

Using the identity: a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

Here a = x, b = 2y, c = 4z.

=  (x + 2y + 4z)(x^2 + (2y)^2 + (4z)^2 - (x)(2y) - (2y)(4z) - (4z)(x))

=  (x + 2y + 4z)(x^2 + 4y^2 + 16z^2 - 2xy - 8yz - 4xz)

HOPE IT HELPS!!!!