Questions: a^3 + 64

Transcript text: 2) $a^{3}+64$

Solution

Solution Steps

To factor the expression $a^3 + 64$, we recognize it as a sum of cubes. The sum of cubes formula is $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Here, $b^3 = 64$, so $b = 4$. We can apply the formula to factor the expression.

Step 1: Identify the Expression

We start with the expression $a^3 + 64$. This can be recognized as a sum of cubes, where $64$ is $4^3$.

Step 2: Apply the Sum of Cubes Formula

Using the sum of cubes formula, which states that $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$, we set $x = a$ and $y = 4$. Thus, we can rewrite the expression as: \[ a^3 + 4^3 = (a + 4)(a^2 - 4a + 16) \]

Step 3: Write the Factored Form

The factored form of the expression $a^3 + 64$ is: \[ (a + 4)(a^2 - 4a + 16) \]