Factorise the following expression: $27 x^{3}-64-108 x^{2}+144 x$
(N/A) The given expression is $27 x^{3}-64-108 x^{2}+144 x$.
We can rewrite this expression in the form $a^{3} + b^{3} + 3a^{2}b + 3ab^{2} = (a + b)^{3}$.
Here,$a = 3x$ and $b = -4$.
Substituting these values into the identity:
$27 x^{3}-64-108 x^{2}+144 x = (3x)^{3} + (-4)^{3} + 3(3x)^{2}(-4) + 3(3x)(-4)^{2}$.
This simplifies to $(3x - 4)^{3}$.
Thus,the factorised form is $(3x - 4)(3x - 4)(3x - 4)$.
We can rewrite this expression in the form $a^{3} + b^{3} + 3a^{2}b + 3ab^{2} = (a + b)^{3}$.
Here,$a = 3x$ and $b = -4$.
Substituting these values into the identity:
$27 x^{3}-64-108 x^{2}+144 x = (3x)^{3} + (-4)^{3} + 3(3x)^{2}(-4) + 3(3x)(-4)^{2}$.
This simplifies to $(3x - 4)^{3}$.
Thus,the factorised form is $(3x - 4)(3x - 4)(3x - 4)$.
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