We #160;have #160;8x3+27y3+125z3 90xyz=2x3+3y3+5z3 3 #215;2x #215;3y #215;5z=2x+3y+5z2x2+3y2+5z2 2x #215;3y 3y #215;5z 5z #215;2x=2x+3y+5z4x2+9y ...

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(x±a)(x±b) = x²±(a+b)x+ab.

8x3+27y3+125z...

Question

$8 x^{3} + 27 y^{3} + 125 z^{3} - 90 x y z$

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Solution

$We have 8 x^{3} + 27 y^{3} + 125 z^{3} - 90 x y z = {(2 x)}^{3} + {(3 y)}^{3} + {(5 z)}^{3} - 3 \times (2 x) \times (3 y) \times (5 z) = (2 x + 3 y + 5 z) [{(2 x)}^{2} + {(3 y)}^{2} + {(5 z)}^{2} - (2 x) \times (3 y) - (3 y) \times (5 z) - (5 z) \times (2 x)] = (2 x + 3 y + 5 z) (4 x^{2} + 9 y^{2} + 25 z^{2} - 6 x y - 15 y z - 10 x z)$

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