alleryStart learning →According to the Sum and Difference of Cubes Pattern, how does a^3+b^3 factor?
A(a+b)(a^2+ab+b^2)
B(a+b)(a^2-ab+b^2)
C(a-b)(a^2+ab+b^2)
D(a+b)(a^2-2ab+b^2)
Answer & Solution
Correct answer: B. (a+b)(a^2-ab+b^2)
1. The sum of cubes pattern factors a cubed + b cubed into a binomial times a trinomial.
2. The binomial factor keeps the same sign as the original expression: (a + b).
3. The trinomial factor is a squared minus ab plus b squared, with the middle term's sign opposite the sign in the original binomial.
4. Changing the binomial to (a - b), keeping a plus sign on ab, or doubling the ab term all break the pattern.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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