# How do you simplify (4x^2 - 1)(x^2 - 6x + 9)?

Feb 7, 2017

$4 {x}^{4} - 24 {x}^{3} + 35 {x}^{2} + 6 x - 9$

#### Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket.
This can be done as shown.

$\left(\textcolor{red}{4 {x}^{2} - 1}\right) \left({x}^{2} - 6 x + 9\right)$

$= \textcolor{red}{4 {x}^{2}} \left({x}^{2} - 6 x + 9\right) \textcolor{red}{- 1} \left({x}^{2} - 6 x + 9\right)$

distributing.

$= \textcolor{b l u e}{4 {x}^{4}} \textcolor{red}{- 24 {x}^{3}} \textcolor{m a \ge n t a}{+ 36 {x}^{2}} \textcolor{m a \ge n t a}{- {x}^{2}} \textcolor{g r e e n}{+ 6 x} \textcolor{p u r p \le}{- 9}$

collecting like terms.

=color(blue)(4x^4)color(red)(-24x^3)color(magenta)(+(36x^2-x^2)color(green)(+6x)color(purple)(-9)

$= 4 {x}^{4} - 24 {x}^{3} + 35 {x}^{2} + 6 x - 9$