Question

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

Answer 1

`4x^4-24x^3+35x^2+6x-9`

Explanation:

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

`(color(red)(4x^2-1))(x^2-6x+9)`

`=color(red)(4x^2)(x^2-6x+9)color(red)(-1)(x^2-6x+9)`

distributing.

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

collecting like terms.

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

`=4x^4-24x^3+35x^2+6x-9`