Which expression is the completely factored form of x^3+8y^6

Answer 1

To factor the expression \( x^3 + 8y^6 \), we can recognize that it is a sum of cubes. The given expression can be rewritten as:

\[ x^3 + (2y^2)^3 \]

We can use the sum of cubes factoring formula, which states that:

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

In our case, \( a = x \) and \( b = 2y^2 \). Plugging these values into the formula, we get:

1. First Term: \( a + b = x + 2y^2 \)
2. Second Term: \( a^2 = x^2 \), \( ab = x(2y^2) = 2xy^2 \), and \( b^2 = (2y^2)^2 = 4y^4 \)

Putting it all together, the completely factored form of \( x^3 + 8y^6 \) is:

\[ (x + 2y^2)(x^2 - 2xy^2 + 4y^4) \]

So, the final answer is:

\[ (x + 2y^2)(x^2 - 2xy^2 + 4y^4) \]