Factors of $$ 8 x^{3}+27 y^{3} $$ are:

Question

UpStudy AI · Accepted Answer

To factor the expression $$ 8x^3 + 27y^3 $$, we can recognize that it is a sum of cubes. The general formula for factoring a sum of cubes $$ a^3 + b^3 $$ is:

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

In our case, we can identify:

- $$ a = 2x $$ (since $$ (2x)^3 = 8x^3 $$)
- $$ b = 3y $$ (since $$ (3y)^3 = 27y^3 $$)

Now, we can apply the sum of cubes formula:

1. Calculate $$ a + b $$:
   $$
   a + b = 2x + 3y
   $$

2. Calculate $$ a^2 $$:
   $$
   a^2 = (2x)^2 = 4x^2
   $$

3. Calculate $$ ab $$:
   $$
   ab = (2x)(3y) = 6xy
   $$

4. Calculate $$ b^2 $$:
   $$
   b^2 = (3y)^2 = 9y^2
   $$

5. Now, substitute these into the second part of the formula:
   $$
   a^2 - ab + b^2 = 4x^2 - 6xy + 9y^2
   $$

Putting it all together, we have:

$$
8x^3 + 27y^3 = (2x + 3y)(4x^2 - 6xy + 9y^2)
$$

Thus, the factors of $$ 8x^3 + 27y^3 $$ are:

$$
(2x + 3y)(4x^2 - 6xy + 9y^2)
$$
The factors of $$ 8x^3 + 27y^3 $$ are $$ (2x + 3y) $$ and $$ (4x^2 - 6xy + 9y^2) $$.

Factors of \( 8 x^{3}+27 y^{3} \) are:

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions