# How do you factor x^4-4x^2?

Nov 15, 2016

${x}^{4} - 4 {x}^{2} = \left({x}^{2} + 2 x\right) \left({x}^{2} - 2 x\right)$

#### Explanation:

• 2 terms
• minus sign
• perfect squares
• even indices

These tell us that we are working with the Difference of Squares

The classic example states: $\text{ } {x}^{2} - {y}^{2} = \left(x + y\right) \left(x - y\right)$

${x}^{4} - 4 {x}^{2} = \left({x}^{2} + 2 x\right) \left({x}^{2} - 2 x\right)$

The biggest difficulty is learning to recognise it for what it is.

Knowing some of the perfect squares by heart is a good start:

$1 \text{ "4" "9" "16" "25" "36" "49" "64" "81" "100" "121" } 144$