How do you simplify 3x^2(3x^2 - x - 2)?

Dec 22, 2016

$9 {x}^{4} - 3 {x}^{3} - 6 {x}^{2}$

Explanation:

To simplify this expression you need to multiply the term outside the parenthesis ($\textcolor{red}{3 {x}^{2}}$) by each term within the parenthesis:

$\left(\textcolor{red}{3 {x}^{2}} \cdot 3 {x}^{2}\right) - \left(\textcolor{red}{3 {x}^{2}} \cdot x\right) - \left(\textcolor{red}{3 {x}^{2}} \cdot 2\right)$

$\left(3 \cdot 3 \cdot {x}^{2} \cdot {x}^{2}\right) - \left(3 \cdot {x}^{2} \cdot x\right) - \left(3 \cdot 2 \cdot {x}^{2}\right)$

We can now use the following rule for exponents to multiply the individual terms:

$\textcolor{red}{{x}^{a} \cdot {x}^{b} = {x}^{a + b}}$

Hint: remember $\textcolor{g r e e n}{x = {x}^{1}}$

$9 {x}^{2 + 2} - 3 {x}^{2 + 1} - 6 {x}^{2}$

$9 {x}^{4} - 3 {x}^{3} - 6 {x}^{2}$