factor: 8x^3 + 1
sum of cubes:
(2x+1)(4x^2-2x+1)
@Steve how did you arrive at this answer?
experience.
sum of cubes:
(a^3±b^3) = (a+b)(a^2∓ab+b^2)
just one of those shortcuts it's helpful to know. Just like
(a^2-b^2)=(a+b)(a-b)
To factor the expression 8x^3 + 1, we can use the sum of cubes formula. The sum of cubes formula is a special factorization pattern that can be used when we have an expression in the form a^3 + b^3.
The sum of cubes formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
In our case, we have 8x^3 + 1, which can be written as (2x)^3 + 1^3.
Now we can apply the sum of cubes formula:
a = 2x
b = 1
Substituting these values into the formula, we get:
(2x)^3 + 1^3 = (2x + 1)(4x^2 - 2x + 1)
Therefore, the factored form of 8x^3 + 1 is (2x + 1)(4x^2 - 2x + 1).