# How do you write (5x^2 - 4x + 5) (3x^2 - 6x + 2) in standard form?

Jan 17, 2017

$15 {x}^{4} - 42 {x}^{3} + 49 {x}^{2} - 38 x + 10$

#### Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket. This is illustrated below.

$\left(\textcolor{red}{5 {x}^{2} - 4 x + 5}\right) \left(3 {x}^{2} - 6 x + 2\right)$

$= \textcolor{red}{5 {x}^{2}} \left(3 {x}^{2} - 6 x + 2\right) \textcolor{red}{- 4 x} \left(3 {x}^{2} - 6 x + 2\right)$
$\textcolor{w h i t e}{\times \times} \textcolor{red}{+ 5} \left(3 {x}^{2} - 6 x + 2\right)$

distributing gives.

$15 {x}^{4} - 30 {x}^{3} + 10 {x}^{2} - 12 {x}^{3} + 24 {x}^{2} - 8 x + 15 {x}^{2} - 30 x + 10$

collecting like terms.

$15 {x}^{4} + \left(- 30 - 12\right) {x}^{3} + \left(10 + 24 + 15\right) {x}^{2} + \left(- 8 - 30\right) x + 10$

$= 15 {x}^{4} - 42 {x}^{3} + 49 {x}^{2} - 38 x + 10 \leftarrow \text{ in standard form}$

Writing in standard form means, start with the term of the highest power of the variable, followed by terms with decreasing powers of the variable.