# What is the standard form of a polynomial (y-2)(y^2+2y+3)?

Jan 25, 2017

To transform this to the standard form we must first multiply each term in the left parenthesis by each term in the right parenthesis:
To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{y} - \textcolor{red}{2}\right) \left(\textcolor{b l u e}{{y}^{2}} + \textcolor{b l u e}{2 y} + \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{y} \times \textcolor{b l u e}{{y}^{2}}\right) + \left(\textcolor{red}{y} \times \textcolor{b l u e}{2 y}\right) + \left(\textcolor{red}{y} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{{y}^{2}}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{2 y}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{3}\right)$

${y}^{3} + 2 {y}^{2} + 3 y - 2 {y}^{2} - 4 y - 6$

We can now group and combine like terms:

#y^3 + 2y^2 - 2y^2 + 3y - 4y - 6

${y}^{3} + \left(2 - 2\right) {y}^{2} + \left(3 - 4\right) y - 6$

${y}^{3} + 0 {y}^{2} - 1 y - 6$

${y}^{3} - y - 6$