Browse Questions

# Write the general term in the expansion of $(x^2 - yx)^{12},\; x\neq 0$

$\begin{array}{1 1} -\;^{12} \large C_r\;x^{24-r} y^r \\-\;^{12} \large C_r\;x^{24-2r} y^r \\-\;^{12} \large C_r\;x^{12-r} y^r \\ -\;^{12} \large C_r\;x^{24-2r} y^{2r} \end{array}$

Toolbox:
• $(a+b)^n = \large \sum \limits_{k=0}^{n}\; $$^n \large C$$_k \; a^{n-k}b^k =\; ^n \large C$$_0\;a^nb^0 +\; ^n \large C$$_1\;a^{n-1}b^1+.... ^n\large C$$_n\;a^0b^n, where b^0 = 1 = a^{n-n} • Looking at the pattern of the successive terms we can say that the (r + 1)\text{th} term T_{r+1} = ^n\large C$$_r\;a^{n–r}b^r$. This is also called the general term of the expansion.