The expression below is a sum of cubes.216x3 + 64A.TrueB.FalseSUBMITarrow_backPREVIOUS

To determine whether the expression $216x^3 + 64A$ is a sum of cubes, we need to understand the general form of a sum of cubes, which is given by:

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

Break Down the Problem

1. Identify Terms:

   • The first term is $216x^3$.
   • The second term is $64A$.

2. Determine Cube Roots:

   • Find $a$ such that $a^3 = 216x^3$.
   • Find $b$ such that $b^3 = 64A$.

Relevant Concepts

3. Calculate Cube Roots:
   • For $216x^3$, since $216 = 6^3$, thus $a = 6x$.
   • For $64A$, since $64 = 4^3$, thus $b = 4A^{1/3}$.

Analysis and Detail

4. Combine and Check:
   • Now we can express the given expression as: $(6x)^3 + (4A)^{3}$
   • Thus, the expression is indeed of the form $a^3 + b^3$.

Verify and Summarize

5. Final Confirmation:
   • Since both terms can be expressed as cubes, $216x^3 + 64A$ is a sum of cubes.

Final Answer

The statement is True.