Factorize the following expression
$27 x^{3} + 64 y^{3}$

(3 x + 4 y) (9 x^{2} - 12 x y + 16 y^{2})

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(3 x - 4 y) (9 x^{2} - 12 x y + 16 y^{2})

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(3 x + 4 y) (9 x^{2} + 12 x y + 16 y^{2})

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None of these

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Solution

The correct option is B $(3 x + 4 y) (9 x^{2} - 12 x y + 16 y^{2})$
$(3 x)^{3} + (4 y)^{3}$

Using $a^{3} + b^{3}$ $= (a^{2} - a b + b^{2}) (a + b)$ , we get

$= (9 x^{2} - 12 x y + 16 y^{2}) (3 x + 4 y)$

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Similar questions

Q. Evaluate:

(3 x + 4 y) (3 x - 4 y) (9 x^{2} + 16 y^{2})

is equal to

81 x^{4} - 256 y^{4}

If true then enter

1

and if false then enter

0

Find the following products:

(i) (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

(ii) (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

(iii) (2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)

(iv) (3x − 4y + 5z) (9x² +16y²+ 25z² + 12xy −15zx + 20yz)