Factorise the following expression: $8x^3 + 343y^3 + 84x^2y + 294xy^2$.
(N/A) The given expression is $8x^3 + 343y^3 + 84x^2y + 294xy^2$.
We can rewrite this as $(2x)^3 + (7y)^3 + 3(2x)^2(7y) + 3(2x)(7y)^2$.
This expression is in the form of the algebraic identity $a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^3$,where $a = 2x$ and $b = 7y$.
Substituting these values,we get $(2x + 7y)^3$.
Thus,the factorised form is $(2x + 7y)(2x + 7y)(2x + 7y)$.
We can rewrite this as $(2x)^3 + (7y)^3 + 3(2x)^2(7y) + 3(2x)(7y)^2$.
This expression is in the form of the algebraic identity $a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^3$,where $a = 2x$ and $b = 7y$.
Substituting these values,we get $(2x + 7y)^3$.
Thus,the factorised form is $(2x + 7y)(2x + 7y)(2x + 7y)$.
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