Question

What is the 8th term in the expansion of (x + 2y)^10?

Answer 1

do the binomial expansion for it
recall that whilst one exponent starts off big, and goes to 0
the other starts off at 0 and goes up

\(\large (x + 2y)^{10}
\\ \quad \\
x^{10}(2y)^0\\
+10(x)^9(2y)^1\\
+\square(x)^8(2y)^2\\
+\square(x)^7(2y)^3\\
+\square(x)^6(2y)^4\\
+\square(x)^5(2y)^5 \\
+\square(x)^4(2y)^6\\
+\square(x)^3(2y)^7\\
+\square(x)^2(2y)^8\\
+\square(x)^1(2y)^9\\
+\square(x)^0(2y)^{10}\)

the coefficient for the next term is
current coefficient, times exponent of 1st term
divided by exponent of 2nd term +1

Answer 2

@jdoe0001 I asked for the answer, not how to find it. What is the 8th term in the expansion (x + 2y)^10?

Answer 3

Just look for the tenth line of the pascal triangle, it goes as follows:
1 10 45 120 210 252 210 120 45 10 1
The eight term is 120.