We have #10; #10;Part (1): #10; #10; 64x^3 729y^3 #10; #10; ( 4x )^3 ( 9y )^3 #10; #10;Using ( x^3 y^3)=( x y #10;)( x^2+y^2+x ...

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Algebraic Identities

Solve 64x3-...

Question

Solve $64 x^{3} - 729 y^{3}$

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Solution

we have

Part (1):-

$64 x^{3} - 729 y^{3}$

${(4 x)}^{3} - {(9 y)}^{3}$

Using $(x^{3} - y^{3}) = (x - y) (x^{2} + y^{2} + x y)$

${(4 x)}^{3} - {(9 y)}^{3} = (4 x - 9 y) [{(4 x)}^{2} + {(9 y)}^{2} + 4 x \times 9 y]$

$= (4 x - 9 y) (16 x^{2} + 81 y^{2} + 36 x y)$

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