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

March 30, 2026Mathematics

ScanSolve AI Answer

March 30, 2026

Answer

4 $,$ b=3x $, and$ n=\frac{1}{2}$.

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

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Write down the first four terms of the binomial expansion of (4+3x)^(1)/(2). The binomial expansion for (a+b)^n is a^n + na^n-1b + (n(n-1))/(2!)a^n-2b^2 + (n(n-1)(n-2))/(3!)a^n-3b^3 + .

Asked on March 30, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 30, 2026

Step 1: Write down the first four terms of the binomial expansion of (4+3x)^(1)/(2). The binomial expansion for (a+b)^n is a^n + na^n-1b + (n(n-1))/(2!)a^n-2b^2 + (n(n-1)(n-2))/(3!)a^n-3b^3 + . Alternatively, we can factor out a to get a^n(1+(b)/(a))^n. In this case, a=4, b=3x, and n=(1)/(2). (4+3x)^