The correct option is A (3y+5z)(9y^2 15yz+25z^2) We have, 27y^3+125z^3=(3y)^3+(5z)^3 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Algebraic Identities

Factorise 2...

Question

Factorise $27 y^{3} + 125 z^{3}$

(3 y + 5 z) (9 y^{2} - 15 y z + 25 z^{2})

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(3 y - 5 z) (9 y^{2} - 15 y z + 25 z^{2})

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(3 y + 5 z) (9 y^{2} + 15 y z + 25 z^{2})

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None of the above

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Solution

The correct option is A $(3 y + 5 z) (9 y^{2} - 15 y z + 25 z^{2})$
We have, $27 y^{3} + 125 z^{3} = (3 y)^{3} + (5 z)^{3}$
Using $x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
$= (3 y + 5 z) {(3 y)^{2} - (3 y) (5 z) + (5 z)^{2}}$
$= (3 y + 5 z) (9 y^{2} - 15 y z + 25 z^{2})$

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