# Find the coefficient of $x^{17}$ in the expansion of $x^5\cdot (1+x^2)^{12}$

Find the coefficient of $x^{17}$ in the expansion of $x^5\cdot (1+x^2)^{12}$

Help to solve this MCQ problem. I have tried a lot of times but I got the wrong answer.

• What have you tried doing? If you add this to your question, then people won't suggest methods you've already tried, or can point out your mistakes – lioness99a Jun 22 '17 at 7:50
• How do you know that your answer was wrong? Do you know the right answer? Maybe show one of your approaches.. – Dirk Jun 22 '17 at 7:50
• for your control $$x^{29}+12 x^{27}+66 x^{25}+220 x^{23}+495 x^{21}+792 x^{19}+924 x^{17}+792 x^{15}+495 x^{13}+220 x^{11}+66 x^9+12 x^7+x^5$$ – Dr. Sonnhard Graubner Jun 22 '17 at 7:52

Hint. Recall the Binomial Theorem. What is the coefficient of $x^{12}$ of $$(1+x^2)^{12}=\sum_{k=0}^{12}\binom{12}{k}(x^2)^k\;?$$