1. Tardigrade
  2. Question
  3. Mathematics
  4. The coefficient of x4 in the expansion of (1-x2+x3-x4)(1-2 x2)6 is co-prime with

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The coefficient of $x^4$ in the expansion of $\left(1-x^2+x^3-x^4\right)\left(1-2 x^2\right)^6$ is co-prime with

Binomial Theorem

Solution:

$ T_{r+1}$ in $\left(1-2 x^2\right)^6$
${ }^6 C_r(-2)^r \cdot x^{2 r}$
$\therefore$ Coefficient of $x^4$ in $\left(1-x^2+x^3-x^4\right)\left(1-2 x^2\right)^6=1 \times{ }^6 C_2(-2)^2-{ }^6 C_1(-2)-{ }^6 C_0=71$.