Question 145763
{{{(x+4)^3}}} Start with the given expression


{{{(x+4)(x+4)(x+4)}}} Expand



{{{(x^2+8x+16)(x+4)}}} Foil the first two binomials



{{{(x+4)(x^2+8x+16)}}} Rearrange the terms




{{{x(x^2+8x+16)+4(x^2+8x+16)}}} Expand. Remember, {{{(a+b)(c+d+e)}}} expands to {{{a(c+d+e)+b(c+d+e)}}}



{{{(x)*(x^2)+(x)*(8x)+(x)*(16)+(4)*(x^2)+(4)*(8x)+(4)*(16)}}} Distribute.



{{{x^3+8*x^2+16*x+4*x^2+32*x+64}}} Multiply.



{{{x^3+12*x^2+48*x+64}}} Now combine like terms.



So {{{(x+4)^3}}} expands to {{{x^3+12*x^2+48*x+64}}}.



In other words, {{{(x+4)^3=x^3+12*x^2+48*x+64}}}.