# How do you find the product of (t+3)(t^2+4t+7)?

Jan 1, 2018

${t}^{3} + 7 {t}^{2} + 19 t + 21$

#### Explanation:

$\text{each term in the second factor is multiplied by each}$
$\text{term in the first factor}$

$\Rightarrow \left(\textcolor{red}{t + 3}\right) \left({t}^{2} + 4 t + 7\right)$

$= \textcolor{red}{t} \left({t}^{2} + 4 t + 7\right) \textcolor{red}{+ 3} \left({t}^{2} + 4 t + 7\right)$

$\text{distribute the brackets and collect like terms}$

$= {t}^{3} + 4 {t}^{2} + 7 t + 3 {t}^{2} + 12 t + 21$

$= {t}^{3} + 7 {t}^{2} + 19 t + 21$