Section 1
Introduction
Expand each of the expressions.$$(1-2 x)^{5}$$
Expand each of the expressions.$$\left(\frac{2}{x}-\frac{x}{2}\right)^{5}$$
Expand each of the expressions.$$(2 x-3)^{6}$$
Expand each of the expressions.$$\left(\frac{x}{3}+\frac{1}{x}\right)^{5}$$
Expand each of the expressions.$$\left(x+\frac{1}{x}\right)^{6}$$
Using binomial theorem, evaluate each of the following:$$(96)^{3}$$
Using binomial theorem, evaluate each of the following:$$(102)^{5}$$
Using binomial theorem, evaluate each of the following:$$(101)^{4}$$
Using binomial theorem, evaluate each of the following:$$(99)^{5}$$
Using Binomial Theorem, indicate which number is larger $(1.1)^{10000}$ or 1000 .
Find $(a+b)^{4}-(a-b)^{4} .$ Hence, evaluate $(\sqrt{3}+\sqrt{2})^{4}-(\sqrt{3}-\sqrt{2})^{4}$.
Find $(x+1)^{6}+(x-1)^{6} .$ Hence or otherwise evaluate $(\sqrt{2}+1)^{6}+(\sqrt{2}-1)^{6}$.
Show that $9^{n+1}-8 n-9$ is divisible by 64 , whenever $n$ is a positive integer.
Prove that $\sum_{r=0}^{n} 3^{r n} \mathrm{C}_{r}=4^{n} .$