Factor. y ^3 + 729
y ^3 + 729
= y^3 + 9^3
If you were given this question, then surely you must have learned about the "sum of cubes" factoring.
Scale factor of 729 and 343
To factor the expression y^3 + 729, we can first recognize that 729 is a perfect cube. In this case, it is the cube of 9 (9^3 = 729).
So we can now rewrite the expression as y^3 + 9^3.
Next, we can use the sum of cubes formula, which states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
Applying this formula to our expression, we have:
y^3 + 9^3 = (y + 9)(y^2 - y*9 + 9^2)
Simplifying the second term, we get:
y^3 + 9^3 = (y + 9)(y^2 - 9y + 81)
Therefore, the factored form of y^3 + 729 is (y + 9)(y^2 - 9y + 81).