Question

How do you factor: `y= 9x^4 - 12x^2 +4`?

Answer 1

`y=(3x^2-2)^2`

Explanation:

This function can be expressed as a `color(blue)"quadratic function"`

`"use the substitution " u=x^2" and express y as"`

`y=9u^2-12u+4`

Now factorise as a quadratic.

`ac=9xx4" and " b=-12`

Consider the product of the factors which give 36 and sum to
- 12

`"these are " -6" and " -6`

`rArry=9u^2-6u-6u+4`

`" Factorise by grouping"`

`y=color(red)(3u)(3u-2)color(red)(-2)(3u-2)`

`"factor out the " color(blue)"common factor" " of " (3u-2)`

`rArry=(3u-2)(color(red)(3u-2))=(3u-2)^2`

`"change u back into terms of x"`

`rArry=(3x^2-2)^2`