I'm not exactly sure how to factor cubed roots:
8x^3 - 1 = (2x)^3 - 1
that's what i get; can it be simplified anymore?
i'm looking at another one, and i don't know where to start:
x^3 - 2x^2 - 4x +8
hmm, cause u can't pull and x out, no quadratic . . .???
your first one fits the pattern for the difference of cubes
A^3 - B^3 = (A-B)(A^2 + AB + B^2)
so (2x)^3 - 1 = (2x-1)(4x^2 + 2x + 1)
test it by expanding my answer
for you second one, try grouping
I will get you started
x^3 - 2x^2 - 4x +8
= x^2(x-2) - 4(x-2)
= ......
for function operations:
If f(x) = x^2 -4 and g(x) = [square root of] (2x+4)
g(f(a+2)) ---> then
x^2 - 4 +2
x^2 - x
[square root of] (2(x^2 - 2) +4)
= x [square root of] 2
wher does 'a' come from?, but is that right?
the x has been replaced by a+2
so since f(x) = x^2 -4 and g(x) = √ (2x+4)
g(f(x)) = √(2(x^2-4) + 4)
= √(2x^2 -4)
then g(f(a+2))
= √(2(a+2)^2 - 4)
=√(2(a^2 + 4a + 4) - 4)
= √(2a^2 + 8a + 4)
check my algebra, sometimes without writing it down first, I tend to make errors while just working it out only on the screen.
To factor cubed roots, you can use the formula for a difference of cubes factorization, which states that:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
In the given expression:
8x^3 - 1 = (2x)^3 - 1
We can rewrite it as:
(2x)^3 - 1^3
Comparing this with the formula for a difference of cubes, we have:
a = 2x and b = 1
Applying the formula, we get:
(2x - 1)((2x)^2 + (2x)(1) + 1^2)
Simplifying further, we have:
(2x - 1)(4x^2 + 2x + 1)
Therefore, the expression 8x^3 - 1 can be further simplified as (2x - 1)(4x^2 + 2x + 1).