Question 118729


{{{(x^3+x^2+1)(x^2-x-5)}}} Start with the given expression




{{{x^3(x^2-x-5)+x^2(x^2-x-5)+1(x^2-x-5)}}} Expand the expression. Remember for something like {{{(a+b+c)(d+e+f)}}} it expands to {{{a(d+e+f)+b(d+e+f)+c(d+e+f)}}}



{{{(x^3)*(1x^2)+(x^3)*(-1x)+(x^3)*(-5)+(x^2)*(1x^2)+(x^2)*(-1x)+(x^2)*(-5)+(1)*(1x^2)+(1)*(-1x)+(1)*(-5)}}} Distribute



{{{x^5-x^4-5x^3+x^4-x^3-5x^2+x^2-x-5}}} Multiply



{{{-4x^2-6x^3-x+x^5-5}}} Combine like terms




{{{x^5-6x^3-4x^2-x-5}}} Now rearrange the terms in descending order



So {{{(x^3+x^2+1)(x^2-x-5)}}} expands and simplifies to {{{x^5-6x^3-4x^2-x-5}}}.


In other words, {{{(x^3+x^2+1)(x^2-x-5)=x^5-6x^3-4x^2-x-5}}}





If you need more help with multiplying polynomials, check out this <a href="http://calc101.com/webMathematica/long-multiply.jsp">Long Multiplication Calculator</a>