Question

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

Answer 1

`x^4 - 4x^2 = (x^2 +2x)(x^2 - 2x)`

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: `" "x^2 -y^2 = (x+y)(x-y)`

`x^4 - 4x^2 = (x^2 +2x)(x^2 - 2x)`

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" "4" "9" "16" "25" "36" "49" "64" "81" "100" "121" "144`