SOLUTION: 8X^3y^6+27

Question 175719: 8X^3y^6+27
Found 2 solutions by EMStelley, nerdybill:
Answer by EMStelley(208) (Show Source): You can put this solution on YOUR website!
I believe what you are asking is to factor

Notice that each term can be written using cubes.

So we have that

Now, the sum of cubes can be factored as following:

So, here and b=3

Simplified, this is

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
I'm assuming you're asked to factor the expression.
.
Starting with:
8X^3y^6+27
.
Notice, I can rewrite the above as:
(2xy^2)^3+(3)^3
.
Now, it is a "sum of cubes" -- a special factor... where:
a^3 + b^3 = (a + b)(a^2 � ab + b^2)
.
In your case,
a = 2xy^2
b = 3
.
Plugging the above into:
a^3 + b^3 = (a + b)(a^2 � ab + b^2)
we get:
(2xy^2)^3 + 3^3 = (2xy^2 + 3)((2xy^2)^2 � 3(2xy^2) + 3^2)
(2xy^2)^3 + 3^3 = (2xy^2 + 3)(4x^2y^4 � 6xy^2 + 9)

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