Factorise the following expression:
$64 x^{3} + 125 y^{3} + 240 x^{2} y + 300 x y^{2}$
$64 x^{3} + 125 y^{3} + 240 x^{2} y + 300 x y^{2}$
(A) The given expression is $64 x^{3} + 125 y^{3} + 240 x^{2} y + 300 x y^{2}$.
We can rewrite this expression as $(4x)^{3} + (5y)^{3} + 3(4x)^{2}(5y) + 3(4x)(5y)^{2}$.
This is in the form of the algebraic identity $a^{3} + b^{3} + 3a^{2}b + 3ab^{2} = (a + b)^{3}$,where $a = 4x$ and $b = 5y$.
Substituting these values,we get $(4x + 5y)^{3}$.
Therefore,the factorised form is $(4x + 5y)(4x + 5y)(4x + 5y)$.
We can rewrite this expression as $(4x)^{3} + (5y)^{3} + 3(4x)^{2}(5y) + 3(4x)(5y)^{2}$.
This is in the form of the algebraic identity $a^{3} + b^{3} + 3a^{2}b + 3ab^{2} = (a + b)^{3}$,where $a = 4x$ and $b = 5y$.
Substituting these values,we get $(4x + 5y)^{3}$.
Therefore,the factorised form is $(4x + 5y)(4x + 5y)(4x + 5y)$.
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