Answer
$64x^3-48x^2+12x-1$
Work Step by Step
According to the Binomial Theorem or Binomial expansion, the expansion for $(x+y)$ in the any number of power can be calculated as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Let's see how this formula works:
$(4x-1)^3=\displaystyle \binom{3}{0}(4x)^3(-1)^0+\displaystyle \binom{3}{1}(4x^{2})(-1)^1
+\displaystyle \binom{3}{2}(4x)^1(-1)^2+\displaystyle \binom{3}{3}(4x)^0(-1)^3$
or, $=64x^3+3(16x^2)(-1)+3(4x)(1)+(-1)$
or, $=64x^3-48x^2+12x-1$
