Question 557537
{{{f(x)=x^2+2x+8}}} Start with the given function



{{{f(x+9)=(x+9)^2+2(x+9)+8}}} Replace EVERY 'x' with 'x+9'



{{{f(x+9)=x^2+18x+81+2(x+9)+8}}} FOIL



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Side note: {{{(x+9)^2 = (x+9)(x+9) = x*x+x*9+9*x+9*9 = x^2+9x+9x+81 = x^2+18x+81}}}


So {{{(x+9)^2 = x^2+18x+81}}}



We are using the FOIL rule: First, Outer, Inner, Last and this means that we multiply the "first" terms, then the "outer" terms, then the "inner" terms, then finally the "last" terms. We then add up these products.


For a more in-depth look at expanding this, check out <a href="http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.557541.html">this link</a>

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{{{f(x+9)=x^2+18x+81+2x+18+8}}} Distribute



{{{f(x+9)=x^2+20x+107}}} Combine like terms.



So the answer is {{{f(x+9)=x^2+20x+107}}}