Answer
$=125x^3-75x^2+15x-1$
Work Step by Step
Binomial Theorem or Binomial expansion can be defined as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Need to apply the formula to get the Binomial Expansion.
we have
$(5x-1)^3=\displaystyle \binom{3}{0}(5x)^3(-1)^0+\displaystyle \binom{3}{1}(5x^{2})(-1)^1
+\displaystyle \binom{3}{2}(5x)^1(-1)^2+\displaystyle \binom{3}{3}(5x)^0(-1)^3$
$=(125)(x^3)(1)+(3)(25x^2)(-1)+(3)(5x)(1)+(-1)(1)$ $\bf{(Simplify)}$
$=125x^3-75x^2+15x-1$
