Factorise 8x^{3} + 125y^{3} + 343 - 210xy. | vedclass

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(A) The given expression is of the form $a^{3} + b^{3} + c^{3} - 3abc$,where $a = 2x$,$b = 5y$,and $c = 7$.We know the identity: $a^{3} + b^{3} + c^{3

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(A) The given expression is of the form $a^{3} + b^{3} + c^{3} - 3abc$,where $a = 2x$,$b = 5y$,and $c = 7$.
We know the identity: $a^{3} + b^{3} + c^{3} - 3abc = (a + b + c)(a^{2} + b^{2} + c^{2} - ab - bc - ca)$.
Here,$3abc = 3(2x)(5y)(7) = 210xy$.
Substituting the values into the identity:
$8x^{3} + 125y^{3} + 343 - 210xy = (2x + 5y + 7)((2x)^{2} + (5y)^{2} + (7)^{2} - (2x)(5y) - (5y)(7) - (7)(2x))$.
Simplifying the terms:
$= (2x + 5y + 7)(4x^{2} + 25y^{2} + 49 - 10xy - 35y - 14x)$.

Factorise $8x^{3} + 125y^{3} + 343 - 210xy$.

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