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What is the form of the Sum of Cubes identity?

A. [tex]\( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \)[/tex]
B. [tex]\( a^3 + b^3 = (a - b)(a^2 + ab + b^2) \)[/tex]
C. [tex]\( a^3 - b^3 = (a + b)(a^2 + ab + b^2) \)[/tex]
D. [tex]\( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \)[/tex]

Sagot :

GinnyAnswer
To determine the form of the Sum of Cubes identity, let's analyze each given option and recall the standard forms of the sum and difference of cubes:

The Sum of Cubes identity is a well-known algebraic formula that factors a sum of two cubes. Specifically, for any two real numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex], the identity states:

[tex]\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \][/tex]

Now look at the given options:

A. [tex]\( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \)[/tex]

B. [tex]\( a^3 + b^3 = (a - b)(a^2 + ab + b^2) \)[/tex]

C. [tex]\( a^3 - b^3 = (a + b)(a^2 + ab + b^2) \)[/tex]

D. [tex]\( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \)[/tex]

Let's match these options with the identity. The statement in option A directly matches our identity for the sum of cubes.

Therefore, the correct form of the Sum of Cubes identity is:

[tex]\[ \boxed{a^3 + b^3 = (a + b)(a^2 - ab + b^2)} \][/tex]

So, the correct choice is Option A.
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