What is $125 x^{9} + 64 y^{12}$ $125x^9+64y^12$ written as a sum of cubes?

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What is $125 x^{9} + 64 y^{12}$ $125x^9+64y^12$ written as a sum of cubes?

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Answer 1 · 2017-12-19T03:21:48

( $5 x^{3}$ $5x^3$ + $4 y^{4}$ $4y^4$ )( $25 x^{6}$ $25x^6$ - $20 x^{3}$ $20x^3$ $y^{4}$ $y^4$ + $16 y^{8}$ $16y^8$ )

Explanation:

The skeletal equation for the sum of cubes:
$a^{3}$ $a^3$ + $b^{3}$ $b^3$ = ( $a$ $a$ + $b$ $b$ )( $a^{2}$ $a^2$ - $a b$ $ab$ + $b^{2}$ $b^2$ )

In the expression $125 x^{9}$ $125x^9$ + $64 y^{12}$ $64y^12$ ,
a = $\sqrt[3]{}$ $root(3)$ ( $125 x^{9}$ $125x^9$ ) = $5 x^{3}$ $5x^3$ and
b = $\sqrt[3]{}$ $root(3)$ ( $64 y^{12}$ $64y^12$ ) = $4 y^{4}$ $4y^4$

Now, plug in the a and b values into the skeletal equation:

$125 x^{9}$ $125x^9$ + $64 y^{12}$ $64y^12$ = ( $5 x^{3}$ $5x^3$ + $4 y^{4}$ $4y^4$ )( $25 x^{6}$ $25x^6$ - $20 x^{3}$ $20x^3$ $y^{4}$ $y^4$ + $16 y^{8}$ $16y^8$ )

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What is $125 x^{9} + 64 y^{12}$ $125x^9+64y^12$ written as a sum of cubes?

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What is 125x9+64y12125x^9+64y^12 written as a sum of cubes?

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What is $125 x^{9} + 64 y^{12}$ $125x^9+64y^12$ written as a sum of cubes?