Answer :
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.
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.
