# How do you use the binomial series to expand (1 + 3x) ^8?

##### 1 Answer
Apr 15, 2018

Pascal's triangle.

#### Explanation:

Since you're taking the binomial to the 8th power you would use the 8th row of this triangle and say that

$1 \left(1\right) \left(3 x\right) + 8 \left(1\right) \left(3\right) x + 28 \left(1\right) \left(3 x\right) + 56 \left(1\right) \left(3 x\right) + 70 \left(1\right) \left(3 x\right) + 56 \left(1\right) \left(3 x\right) + 28 \left(1\right) \left(3 x\right) + 8 \left(1\right) \left(3 x\right) + 1 \left(1\right) \left(3 x\right)$

and then add your exponents in a descending order so

$1 {\left(1\right)}^{8} {\left(3 x\right)}^{0} + 8 {\left(1\right)}^{7} {\left(3 x\right)}^{1} + 28 {\left(1\right)}^{6} {\left(3 x\right)}^{2} + 56 {\left(1\right)}^{5} {\left(3 x\right)}^{3} + 70 {\left(1\right)}^{4} {\left(3 x\right)}^{4} + 56 {\left(1\right)}^{3} {\left(3 x\right)}^{5} + 28 {\left(1\right)}^{2} {\left(3 x\right)}^{6} + 8 {\left(1\right)}^{1} {\left(3 x\right)}^{7} + 1 {\left(1\right)}^{0} {\left(3 x\right)}^{8}$

and simplify.