Question
47-48: Simplifying a Difference Quotient Simplify using theBinomial Theorem.$$\frac{(x+h)^{3}-x^{3}}{h}$$
Step 1
We can use the Binomial Theorem to do this. The Binomial Theorem states that $(a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2}a^{n-2}b^{2}+...+b^{n}$. In our case, $a=x$, $b=h$, and $n=3$. So, we get: $$(x+h)^{3}=x^{3}+3x^{2}h+3xh^{2}+h^{3}$$ Show more…
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