Question 118881
#1





{{{(x^3+2x+1)(2x^2-4x-5)}}} Start with the given expression




{{{x^3(2x^2-4x-5)+2x(2x^2-4x-5)+1(2x^2-4x-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)*(2x^2)+(x^3)*(-4x)+(x^3)*(-5)+(2x)*(2x^2)+(2x)*(-4x)+(2x)*(-5)+(1)*(2x^2)+(1)*(-4x)+(1)*(-5)}}} Distribute



{{{2x^5-4x^4-5x^3+4x^3-8x^2-10x+2x^2-4x-5}}} Multiply



{{{-4x^4-6x^2-x^3-14x+2x^5-5}}} Combine like terms




{{{2x^5-4x^4-x^3-6x^2-14x-5}}} Now rearrange the terms in descending order



So {{{(x^3+2x+1)(2x^2-4x-5)}}} expands and simplifies to {{{2x^5-4x^4-x^3-6x^2-14x-5}}}.


In other words, {{{(x^3+2x+1)(2x^2-4x-5)=2x^5-4x^4-x^3-6x^2-14x-5}}}





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#2



{{{(x-2)(x+7)(2x+3)}}} Start with the given expression


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First let's foil {{{(x-2)(x+7)}}}





{{{(x-2)(x+7)}}} Start with the given expression




Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(x)-2)(highlight(x)+7)}}} Multiply the First terms:{{{(x)*(x)=x^2}}}



{{{(highlight(x)-2)(x+highlight(7))}}} Multiply the Outer terms:{{{(x)*(7)=7x}}}



{{{(x+highlight(-2))(highlight(x)+7)}}} Multiply the Inner terms:{{{(-2)*(x)=-2x}}}



{{{(x+highlight(-2))(x+highlight(7))}}} Multiply the Last terms:{{{(-2)*(7)=-14}}}



{{{x^2+7x-2x-14}}} Now collect every term to make a single expression




{{{x^2+5x-14}}} Now combine like terms




So {{{(x-2)(x+7)}}} foils and simplifies to  {{{x^2+5x-14}}}




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So  our expression then becomes



{{{(x^2+5x-14)(2x+3)}}}






Now let's multiply out {{{(x^2+5x-14)(2x+3)}}}


{{{(x^2+5x-14)(2x+3)}}} Start with the given expression




{{{x^2(2x+3)+5x(2x+3)-14(2x+3)}}} Expand the expression. Remember for something like {{{(a+b+c)(d+e)}}} it expands to {{{a(d+e)+b(d+e)+c(d+e)}}}



{{{(x^2)*(2x)+(x^2)*(3)+(5x)*(2x)+(5x)*(3)+(-14)*(2x)+(-14)*(3)}}} Distribute



{{{2x^3+3x^2+10x^2+15x-28x-42}}} Multiply



{{{13x^2+2x^3-13x-42}}} Combine like terms




{{{2x^3+13x^2-13x-42}}} Now rearrange the terms in descending order



So {{{(x-2)(x+7)(2x+3)}}} expands and simplifies to {{{2x^3+13x^2-13x-42}}}.


In other words, {{{(x-2)(x+7)(2x+3)=2x^3+13x^2-13x-42}}}





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