The correct option is A (4m 7n)(16m^2+28mn+49n^2) We have, 64m^3 343n^3=(4m)^3 (7n)^3 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Algebraic Identities

Factorise 6...

Question

Factorise $64 m^{3} - 343 n^{3}$

(4 m + 7 n) (16 m^{2} - 28 m n + 49 n^{2})

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(4 m - 7 n) (16 m^{2} + 28 m n + 49 n^{2})

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(4 m + 7 n) (16 m^{2} + 28 m n + 49 n^{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(4 m - 7 n) (16 m^{2} - 28 m n + 49 n^{2})

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Solution

The correct option is A. $(4 m - 7 n) (16 m^{2} + 28 m n + 49 n^{2})$
We have, $64 m^{3} - 343 n^{3} = (4 m)^{3} - (7 n)^{3}$
Using $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
Here $x = 4 m$ and $y = 7 n$
$\Rightarrow (4 m)^{3} - (7 n)^{3}$
$= (4 m - 7 n) {(4 m)^{2} + (4 m) (7 n) + (7 n)^{2}}$
$= (4 m - 7 n) (16 m^{2} + 28 m n + 49 n^{2})$

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