Binomial expansion for rational powers Quiz

1. Find the coefficient of $x^2$ in the expansion of $(1-x)^{-2}$.

• A. $2$
• B. $6$
• C. $3$
• D. $-3$

2. For which values of $x$ is the expansion of $(1+3x)^{\frac12}$ valid?

• A. $|x|<\frac13$
• B. $|x|<1$
• C. $|x|<3$
• D. $|x|<\frac19$

3. Find the coefficient of $x^2$ in the expansion of $(1+x)^{\frac12}$.

• A. $\frac18$
• B. $\frac14$
• C. $-\frac14$
• D. $-\frac18$

4. Which expression equals $(9+x)^{\frac12}$ before expanding?

• A. $9\left(1+\frac x9\right)^{\frac12}$
• B. $3(1+x)^{\frac12}$
• C. $3\left(1+\frac x9\right)^{\frac12}$
• D. $\left(1+\frac x9\right)^{\frac12}$

5. For which values of $x$ is the expansion of $\frac{1}{(1+x)(1-2x)}$ valid?

• A. $|x|<1$
• B. $|x|<\frac12$
• C. $|x|<2$
• D. $|x|<\frac32$