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

1 Answer
Apr 16, 2017

Answer:

#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#