alleryStart learning →What happens when you try to factor a sum of squares like a^2 + b^2?
AIt always factors as (a+b)(a-b)
BIt is prime after any GCF is removed
CIt always factors as (a+b)(a+b)
DIt factors only when a equals b
Answer & Solution
Correct answer: B. It is prime after any GCF is removed
1. Sums of squares plainly do not factor into a product of binomials.
2. There are no two binomials that multiply together to produce a plain sum like a squared + b squared, since multiplying conjugates always cancels the middle term into a difference, not a sum.
3. After any GCF has been removed, an expression in the form a squared + b squared is simply prime.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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