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Write down the first four terms of the binomial expansion of (4+3x)^(1)/(2).

Mathematics

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Step 1: Write down the first four terms of the binomial expansion of (4+3x)12(4+3x)^{\frac{1}{2}}.
The binomial expansion for (a+b)n(a+b)^n is an+nan−1b+n(n−1)2!an−2b2+n(n−1)(n−2)3!an−3b3+…a^n + na^{n-1}b + \frac{n(n-1)}{2!}a^{n-2}b^2 + \frac{n(n-1)(n-2)}{3!}a^{n-3}b^3 + \dots.
Alternatively, we can factor out aa to get an(1+ba)na^n(1+\frac{b}{a})^n.
In this case, a=4a=4, b=3xb=3x, and n=12n=\frac{1}{2}.

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