A few days ago
How do I completely factor this polynomial? (x^2+1)^2 -4x^2?
How do I completely factor this polynomial? (x^2+1)^2 -4x^2?
Top 1 Answers
A few days ago
Favorite Answer
Anytime you have the difference of perfect squares (like in your problem), they can be factored as follows:
a^2 – b^2
= (a – b)(a + b)
In your problem, a = (x^2+1) and b = 2x.
(Yes, b = 2x, not 4x since 2x*2x = 4x^2.)
So (x^2+1)^2 -4x^2
= ((x^2+1) – 2x)((x^2+1) + 2x)
= (x^2 – 2x + 1)(x^2 + 2x + 1)
Now both of these are called “perfect square trinomials” because they are the squares of monomials:
= (x-1)(x-1) ( x+1)(x+1)
= (x-1)^2 * (x+1)^2
I hope this helps!
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