Question

Find the third term of the binomial expansion.(4x + y)^5

Answer 1

Using the binomial theorem, we have:

`\begin{gathered} (a+b)^n=nCk\cdot a^(n-1)\cdot b^k \\ \text{ In this case: a=}4x,\text{ b=y, n=5, k=}2 \\ 5C2\cdot(4x)^(5-2)\cdot y^2\text{ (Replacing)} \\ 5C2\cdot(4x)^3\cdot y^2\text{ (Subtracting exponents)} \\ 10\cdot(4x)^3\cdot y^2\text{ (Solving the combination)} \\ \text{ 10}\cdot\text{64}x^3\cdot y^2\text{ (Raising 4x to the power of 3)} \\ \text{640}x^3\cdot y^2\text{ (Multiplying)} \\ \text{The answer is }640x^3\cdot y^2 \end{gathered}`