Factor or can it be factored 64s^3+729x^3
You are in luck with that one. Yes, it can be factored.
It is of the form a^3 + b^3, where a = 4s and b = 9y.
Recall that
a^3 + b^3 = (a + b)(a2 - ab + b2)
So one of the factors is
(4s + 9y)
See if you can figure out the other one.
Thank you I know I can from there.
To determine if the expression 64s^3 + 729x^3 can be factored or not, we need to check if it satisfies any special factoring patterns. In this case, we can use the difference of cubes formula.
The difference of cubes formula states that an expression in the form of a^3 - b^3 can be factored as (a - b)(a^2 + ab + b^2).
Let's see if we can apply the difference of cubes formula to the expression 64s^3 + 729x^3:
64s^3 + 729x^3
This expression consists of two terms, 64s^3 and 729x^3. Notice that neither term is a perfect cube, but we can rewrite them as the cubes of smaller expressions:
64s^3 = (4s)^3
729x^3 = (9x)^3
Now we can factor out the common factors:
64s^3 + 729x^3 = (4s)^3 + (9x)^3
We can identify that the expression can be factored using the difference of cubes formula:
(4s)^3 + (9x)^3 = (4s + 9x)((4s)^2 - (4s)(9x) + (9x)^2)
Simplifying the squared terms:
(4s)^2 = 16s^2
(9x)^2 = 81x^2
(4s + 9x)((4s)^2 - (4s)(9x) + (9x)^2) = (4s + 9x)(16s^2 - 36sx + 81x^2)
Therefore, the expression 64s^3 + 729x^3 can be factored as (4s + 9x)(16s^2 - 36sx + 81x^2).