Question 149487
{{{(2x-3)^3}}} Start with the given expression.



{{{(2x-3)(2x-3)(2x-3)}}} Expand. Remember {{{A^3=A*A*A}}}



{{{(2x-3)(4x^2-12x+9)}}} FOIL the last two terms {{{(2x-3)(2x-3)}}} to get {{{4x^2-12x+9}}}



{{{2x(4x^2-12x+9)-3(4x^2-12x+9)}}} Expand again. Notice how {{{(a+b)(c+d+e)=a(c+d+e)+b(c+d+e)}}}



{{{(2x)(4x^2)+(2x)(-12x)+(2x)(9)+(-3)(4x^2)+(-3)(-12x)+(-3)(9)}}} Distribute.



{{{8x^3-24x^2+18x-12x^2+36x-27}}} Multiply.



{{{8x^3-36x^2+54x-27}}} Combine like terms.



So {{{(2x-3)^3}}} expands and simplifies to {{{8x^3-36x^2+54x-27}}}



In other words, {{{(2x-3)^3=8x^3-36x^2+54x-27}}}