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

Apr 16, 2017

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

Explanation:

This function can be expressed as a $\textcolor{b l u e}{\text{quadratic function}}$

$\text{use the substitution " u=x^2" and express y as}$

$y = 9 {u}^{2} - 12 u + 4$

$a c = 9 \times 4 \text{ and } b = - 12$

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

$\text{these are " -6" and } - 6$

$\Rightarrow y = 9 {u}^{2} - 6 u - 6 u + 4$

$\text{ Factorise by grouping}$

$y = \textcolor{red}{3 u} \left(3 u - 2\right) \textcolor{red}{- 2} \left(3 u - 2\right)$

$\text{factor out the " color(blue)"common factor" " of } \left(3 u - 2\right)$

$\Rightarrow y = \left(3 u - 2\right) \left(\textcolor{red}{3 u - 2}\right) = {\left(3 u - 2\right)}^{2}$

$\text{change u back into terms of x}$

$\Rightarrow y = {\left(3 {x}^{2} - 2\right)}^{2}$