Let f(x) = 4x^2 + x + 1 and g(x) = x^2 – 2. Find g(f(x)). Show each step of your work.

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Let f(x) = 4x^2 + x + 1 and g(x) = x^2 – 2. Find g(f(x)). Show each step of your work.

Mathematics
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PLEASE HELP
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What I have so far: Original: f(x) = 4x^2 + x + 1; g(x) = x^2 – 2 Combine: (4x^2 + x + 1)^2 - 2
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16x^4 + x^2 + 1?
no (a + b + c)^2 = (a + b + c)(a + b + c) not enough terms it might be easier to complete the square
Whatever is easier
do you have choices?
No, this is written.
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16x^4 + 8x^3 + 9x^2 + 2x -1
if might be enough to show the substitution and get the right expression for g(f(x)) or to get the above with the expansion
Wow, okay, so... ((2x)^2 + x + 1)^2 - 2 What's the second row?
do you know how to use the distributive property? some people use FOIL to remember but that is with 2 terms here we have 3 terms inside you need to multiply each term
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Could you type out the second row please?
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simplify this then subtract 2
((2x)^2 + x + 1)^2 - 2 2x^4 + 2(2x)^2 + 8x^2 + (x+1) + (x+1)^2 - 2 16x^4 + 8x^3 + 9x^2 + 2x -1 Is that what you drew?
you did not copy exactly what I had but I think you got the general idea
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Original: f(x) = 4x^2 + x + 1; g(x) = x^2 – 2 Combine: (4x^2 + x + 1)^2 - 2 Factor: (4x^2 + x + 1) (4x^2 + x + 1) - 2 Expand: 16x^4 + 4x^3 + 9x^2 + 4x^3 + x^2 + x + 1 - 2 Solve: 16x^4 + 8x^3 + 9x^2 + 2x -1
not factor expand not expand simplify yes

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