Answer to the 1st part: [tex]6x^2+12xh+6h^2-2x-2h+1[/tex]
Answer to the 2nd part: [tex]12x+6h-2[/tex]
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Work Shown:
Replace every x with (x+h). Expand and simplify
[tex]f(x) = 6x^2-2x+1\\\\f(x+h) = 6(x+h)^2-2(x+h)+1\\\\f(x+h) = 6(x^2+2xh+h^2)-2(x+h)+1\\\\f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\[/tex]
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Subtract off f(x), then divide everything over h. Simplify.
[tex]f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-(6x^2-2x+1)\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-6x^2+2x-1\\\\f(x+h)-f(x) = 12xh+6h^2-2h\\\\\frac{f(x+h)-f(x)}{h} = \frac{12xh+6h^2-2h}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{h(12x+6h-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} = 12x+6h-2\\\\[/tex]
