Question

factorise 64m^3-343n^3

Answer 1

Answer:

(4m-7m)[16m²+28mn+49n²]

Explanation:

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We know the algebraic identity:

a³-b³ = (a-b)(a²+ab+b²)

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Given

64m³ - 343n³

= (4m)³ - (7n)³

= (4m-7m)[(4m)²+(4m)(7n)+(7n)²]

= (4m-7m)[16m²+28mn+49n²]

Therefore,

64m³-343n³

= (4m-7m)[16m²+28mn+49n²]

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Answer 2

Answer:

The factorization is

$64m^3-343n^3=(6m-7n)(36m^2+42mn+49n^2)$

Step-by-step explanation:

Given the expression

$64m^3-343n^3$

we have to factorize the above expression completely.

$64m^3-343n^3=(6m)^3-(7n)^3$

By the identity

$x^3-y^3=(x-y)(x^2+xy+y^2)$

Put x=6m and y=7n

$64m^3-343n^3=(6m-7n)((6m)^2+(6m)(7n)+(7n)^2)$

$=(6m-7n)(36m^2+42mn+49n^2)$