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According to the Difference of Squares Pattern, how does a^2-b^2 factor?
A(a-b)(a-b)
B(a+b)(a+b)
Ca(a-2b)
D(a-b)(a+b)
Answer & Solution
Correct answer: D. (a-b)(a+b)
1. The pattern reverses the Product of Conjugates: multiplying (a - b) and (a + b) gives a squared - b squared.
2. Factoring in reverse, a squared - b squared becomes the product of conjugates (a - b)(a + b).
3. Squaring either binomial instead of pairing opposite signs would produce a trinomial with a middle term, not the original two-term difference.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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