Factorise the following:
$1-64 a^{3}-12 a+48 a^{2}$
$1-64 a^{3}-12 a+48 a^{2}$
(A) The given expression is $1-64 a^{3}-12 a+48 a^{2}$.
We can rewrite this expression as $1^{3}-(4 a)^{3}-3(1)(4 a)(1-4 a)$.
This matches the algebraic identity $(x-y)^{3} = x^{3}-y^{3}-3xy(x-y)$,where $x=1$ and $y=4a$.
Therefore,the expression simplifies to $(1-4 a)^{3}$.
Thus,the factorised form is $(1-4 a)(1-4 a)(1-4 a)$.
We can rewrite this expression as $1^{3}-(4 a)^{3}-3(1)(4 a)(1-4 a)$.
This matches the algebraic identity $(x-y)^{3} = x^{3}-y^{3}-3xy(x-y)$,where $x=1$ and $y=4a$.
Therefore,the expression simplifies to $(1-4 a)^{3}$.
Thus,the factorised form is $(1-4 a)(1-4 a)(1-4 a)$.
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