# How do you simplify the product (x^2 + x - 1)(x + 1) and write it in standard form?

Sep 5, 2016

${x}^{3} + 2 {x}^{2} - 1$

#### Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket.
This can be done as follows.

$\left(\textcolor{red}{{x}^{2} + x - 1}\right) \left(x + 1\right)$

$= \textcolor{red}{{x}^{2}} \left(x + 1\right) \textcolor{red}{+ x} \left(x + 1\right) \textcolor{red}{- 1} \left(x + 1\right)$

distribute each set of brackets.

$= {x}^{3} + {x}^{2} + {x}^{2} + x - x - 1$

and now collect like terms

$\Rightarrow \textcolor{b l u e}{{x}^{3}} \textcolor{red}{+ {x}^{2}} \textcolor{red}{+ {x}^{2}} \textcolor{m a \ge n t a}{\cancel{+ x}} \textcolor{m a \ge n t a}{\cancel{- x}} - 1 = {x}^{3} + 2 {x}^{2} - 1$

$= {x}^{3} + 2 {x}^{2} - 1 \text{ in standard form}$

Standard form means writing the expression beginning with the term which has the highest power of the variable. In this case ${x}^{3}$ then the next term with the next highest power. In this case $+ 2 {x}^{2}$ and so on until the last term.