Question
Which expression is the completely factored form of x^3+8y^6
Answers
GPT-4o mini
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:
\[
(x + 2y^2)(x^2 - 2xy^2 + 4y^4)
\]
\[
x^3 + (2y^2)^3
\]
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:
\[
(x + 2y^2)(x^2 - 2xy^2 + 4y^4)
\]