Answer: [tex]f(\text{x+h}) = \text{x}^2+2\text{x}\text{h}+\text{h}^2[/tex]
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Work Shown:
[tex]f(\text{x}) = \text{x}^2\\\\f(\text{x+h}) = (\text{x+h})^2\\\\f(\text{x+h}) = (\text{x+h})(\text{x+h})\\\\f(\text{x+h}) = \text{x}*\text{x}+\text{x}*\text{h}+\text{h}*\text{x}+\text{h}*\text{h}\\\\f(\text{x+h}) = \text{x}^2+\text{x}\text{h}+\text{x}\text{h}+\text{h}^2\\\\f(\text{x+h}) = \text{x}^2+2\text{x}\text{h}+\text{h}^2\\\\[/tex]
Explanation:
I replaced each copy of x with x+h. Then I used the FOIL rule to expand things out and combine like terms. The distributive property or the box method are two other pathways you can take.
