What is the standard form of y= (x + 2)(x^3 + 216) ?

Apr 15, 2017

See the entire solution process below>

Explanation:

We must multiply the two terms on the right to put this equation into standard form: To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$y = \left(\textcolor{red}{x} + \textcolor{red}{2}\right) \left(\textcolor{b l u e}{{x}^{3}} + \textcolor{b l u e}{216}\right)$ becomes:

$y = \left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{3}}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{216}\right) + \left(\textcolor{red}{2} \times \textcolor{b l u e}{{x}^{3}}\right) + \left(\textcolor{red}{2} \times \textcolor{b l u e}{216}\right)$

$y = {x}^{4} + 216 x + 2 {x}^{3} + 432$

We can now put the $x$ terms in descending order by power:

$y = {x}^{4} + 2 {x}^{3} + 216 x + 432$