Question

Factorise 2х^6– 48root3y^3

Answer 1

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$2x {}^{6} - 48 \sqrt{3} y {}^{3} \\ = 2(x {}^{6} - 24 \sqrt{3} y {}^{3} ) \\ = 2((x {}^{2}) {}^{3} - \sqrt{3} \times \sqrt{3} \times \sqrt{3} \times 2 {}^{3} y {}^{3} ) \\ = 2((x {}^{2}) {}^{3} - (2 \sqrt{3} y) {}^{3} ) \\ = 2(x {}^{2} - 2 \sqrt{3} y)(x {}^{4} + 12y {}^{2} + 2 \sqrt{3} x {}^{2} y)$

Answer 2

Answer:

$\huge\begin{lgathered}2x {}^{6} - 48 \sqrt{3} y {}^{3} \\ = 2(x {}^{6} - 24 \sqrt{3} y {}^{3} ) \\ = 2((x {}^{2}) {}^{3} - \sqrt{3} \times \sqrt{3} \times \sqrt{3} \times 2 {}^{3} y {}^{3} ) \\ = 2((x {}^{2}) {}^{3} - (2 \sqrt{3} y) {}^{3} ) \\ = 2(x {}^{2} - 2 \sqrt{3} y)(x {}^{4} + 12y {}^{2} + 2 \sqrt{3} x {}^{2} y)\end{lgathered}$