Explain how did we get f(x+h)2

July 9, 2026Mathematics

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Answer

x^2 + 2xh + h^2

3 steps

It seems there might be a slight misunderstanding in the notation. For the function $f(x) = x^2$ , we are looking for $f(x+h)$ , not $f(x+h)^2$ .

Here's how we get $f(x+h)$ :

Understand the function definition.
The function is defined as $f(\text{input}) = (\text{input})^2$ . Whatever is inside the parentheses of $f(\cdot)$ gets squared.
Substitute $(x+h)$ as the input.
When we want to find $f(x+h)$ , we replace every instance of $x$ in the original function $f(x) = x^2$ with $(x+h)$ .
So, $f(x+h) = (x+h)^2$ .
Expand the expression $(x+h)^2$ .
This is a standard algebraic expansion:
$(x+h)^2 = (x+h)(x+h)$ $(x+h)^2 = x \cdot x + x \cdot h + h \cdot x + h \cdot h$ $(x+h)^2 = x^2 + xh + xh + h^2$ $(x+h)^2 = x^2 + 2xh + h^2$
So, $f(x+h)$ is equal to $\boxed{x^2 + 2xh + h^2}$ .

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