# How do you simplify the product (2n - 3)(n^2 - 2n + 5) and write it in standard form?

May 11, 2017

2n^3-7n^2+16n-15"

#### Explanation:

Multiply each term in the second bracket by each term in the first bracket as shown below.

$\left(\textcolor{red}{2 n - 3}\right) \left({n}^{2} - 2 n + 5\right)$

$= \textcolor{red}{2 n} \left({n}^{2} - 2 n + 5\right) \textcolor{red}{- 3} \left({n}^{2} - 2 n + 5\right)$

$= \left(\textcolor{red}{2 n} \times {n}^{2}\right) + \left(\textcolor{red}{2 n} \times - 2 n\right) + \left(\textcolor{red}{2 n} \times 5\right)$

$\textcolor{w h i t e}{=} + \left(\textcolor{red}{- 3} \times {n}^{2}\right) + \left(\textcolor{red}{- 3} \times - 2 n\right) + \left(\textcolor{red}{- 3} \times 5\right)$

$= 2 {n}^{3} - 4 {n}^{2} + 10 n - 3 {n}^{2} + 6 n - 15$

$= 2 {n}^{3} - 7 {n}^{2} + 16 n - 15 \leftarrow \text{ in standard form}$