Question

What is the sixth term of (2x - 3y)11?

Answer 1

you mean
\[(2x-3y)^{11}\] ???

Answer 2

Using the Binomial Theorem we look at the 11th row of PASCALS TRIANGLE (because your expression has a power to a 11)
\[1* (2x)^{11} * (-3y)^{0}\]
\[11 * (2x)^{10} * (-3y)^{^{1}}\]
\[55* (2x)^{9}* (-3y)^2\]
\[165 * (2x)^{8} * (-3y)^{3}\]
\[330 * (2x)^{7} * (-3y)^{4}\]
\[462 * (2x)^{6} * (-3y)^{5}\] The last one I typed is the 6th term.
Simplfying: \[462*64x ^{6}*-243y ^{5}\]
\[6th term: -7185024x ^{6}y ^{5}\]