Factoring with repeated use of difference of squares:
Recall that a difference of squares means one perfect square term minus another perfect square term, and they factor as follows:
Example:
Recall also that a sum of squares does not factor over the real numbers.
Example:
This objective involves factoring a difference of squares that leaves you with a factor that is itself a difference of squares.
Example:
Notice first that this is different from the example above in that w is raised to the fourth power.
Secondly, notice that the blue factor is also a difference of square so we want to factor it again to get a final answer of
The last factor is a sum of squares so we cannot do anything further to it.
Another example:
We first note that neither 48 nor 3 are perfect squares, BUT we can factor out a greatest common factor of 3x2 to get a factor that is a difference of squares:
Notice the last factor is a difference of squares so we need to factor it again to get a final answer of
