How can i factorize this?
8x^3+1
8x^3+ 1
(2x)³+1³
2x+1
X=1/2
use A^3 + B^3 = (A+B)(A^2 - AB + B^2)
(memorize it)
We call it the sum of cubes,
we can also factor the difference of cubes.
8x^3 is a perfect cube and so is 1, so the expression fits the formula
8x^3+ 1
= (2x + 1)(4x^2 - 2x + 1)
To factorize the expression 8x^3 + 1, we can use the sum of cubes formula. The sum of cubes formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
In this case, our expression is 8x^3 + 1. We can see that 8 is the cube of 2, and x^3 is the cube of x. So, we can rewrite the expression as (2x)^3 + 1^3.
Using the sum of cubes formula, we have:
(2x + 1)((2x)^2 - (2x)(1) + 1^2)
Simplifying, we get:
(2x + 1)(4x^2 - 2x + 1)
So, the factorization of 8x^3 + 1 is (2x + 1)(4x^2 - 2x + 1).