Question

question 1 of 10
what is the form of the sum of cubes identity?

a. $a^3 + b^3 = (a - b)\left(a^2 + ab + b^2\
ight)$

b. $a^3 + b^3 = (a + b)\left(a^2 - ab + b^2\
ight)$

c. $a^3 - b^3 = (a - b)\left(a^2 + ab + b^2\
ight)$

d. $a^3 - b^3 = (a + b)\left(a^2 + ab + b^2\
ight)$

Explanation:

The Sum of Cubes identity states that the sum of two cubes \(a^3 + b^3\) factors into a binomial \((a + b)\) multiplied by a trinomial \((a^2 - ab + b^2)\). Option A incorrectly uses \((a - b)\) as the binomial factor. Option C is the Difference of Cubes identity, not Sum of Cubes. Option D has an incorrect binomial factor for the difference of cubes.

Answer:

B. \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)