Question

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

Answer 1

հҽվ!

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${x}^{3} + 8{y}^{3} + 64{z}^{3} - 24xyz \\ \\ By \: Factorising \\ \\ {x}^{3} + {(2y)}^{3} + {(4z)}^{3} - 3(x)(2y(4z) \\ \\ (x + 2y + 4z) ({x}^{2} +4{y}^{2} + 16{z}^{2} - 2xy -8yz -4xz)$

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Answer 2

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

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

It is in the form of 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!