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

1 Answer
Nov 15, 2016

Answer:

#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#