Factor $$ 8 h^{3}+g^{3} $$ completely

Question

UpStudy AI · Accepted Answer

To factor the expression $$ 8h^{3} + g^{3} $$ completely, we can recognize it as a sum of cubes:

$$
8h^{3} + g^{3} = (2h)^{3} + g^{3}
$$

The sum of cubes formula is:

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

Applying this formula:

$$
(2h)^{3} + g^{3} = (2h + g)\left((2h)^{2} - (2h)(g) + g^{2}\right)
$$

Simplifying the terms inside the parentheses:

$$
(2h + g)(4h^{2} - 2hg + g^{2})
$$

So, the completely factored form is:

$$
(2h + g)(4h^{2} - 2hg + g^{2})
$$

**Answer:**
$$
(2h + g)\left(4h^{2} - 2hg + g^{2}\right)
$$
$$ 8h^{3} + g^{3} = (2h + g)(4h^{2} - 2hg + g^{2}) $$

Factor completely