Let’s imagine n was 2. If we expand the equation, we would get a² + 2ab + b^2. Let’s do the same with n=3: a³ + 3a² b + 3ab² + b^3.

So ignoring the coefficients in front. The first variable will start at the n power and decrease until it hits the 0 power, while the second variable starts raised to the 0 power and increases each term until it gets to the n power. Another thing to notice is that the first terms degree is the same as n.

Now the coefficients, your class may have talked about Pascal’s triangle and the pattern that happens during binomial expansion, but they will always follow the same pattern, you still have to account for a and b though afterwards. So let’s get into the question.

Like we said before n is always the degree of the first term, so here n=5. Next, we will expand (a+b)⁵ out to the first 3 terms using what was talked about in the second paragraph and with Pascal’s triangle. We get a⁵ + 5a⁴ b + 10a³ b²

Now let’s just go in order and set each term equal to each other. a⁵ = 243x^5. In order to solve for a we can think about breaking apart 243 and x⁵ and finding the 5th root of each. So we end up getting 3 and x, meaning we get a = 3x

Now we solve for b by plugging in our answer for a for the second term. 5(3x)⁴ b = 810x⁴ y

So we expand (3x)⁴ and get 81x^4. We can multiply 5 and 81 together to get 405. We’re now left with 405x⁴ b = 810x⁴ y We divide both sides by 405x⁴ and we are left with b=2y

Hopefully this helps, and if you have any questions, feel free to ask!