To find the solution, we first need to simplify the expression x-5/(4x+8) and then multiply it by (12x^2 + 32x + 16).
1. Simplify x-5/(4x+8):
(x-5)/(4x+8) = (x-5)/4(x+2)
Using the formula a^2 - b^2 = (a+b)(a-b):
= (x+2)(x-2)/4(x+2)
= (x-2)/4
2. Multiply by (12x^2 + 32x + 16):
((x-2)/4)(12x^2 + 32x + 16)
= (12x^3 - 24x^2 + 32x^2 - 64x + 16x - 32)/4
= (12x^3 + 8x - 32)/4
= 3x^3 + 2x - 8
Therefore, the final solution is 3x^3 + 2x - 8.
x-5 over 4x+8 multiply by (12x^2 + 32x + 16)
5 answers
can the solution be simplified or factored
Yes, the solution 3x^3 + 2x - 8 can be factored and simplified further.
To factor the expression, we can look for common factors among the terms, and then see if any terms can be grouped together.
Factoring 3x^3 + 2x - 8:
First, note that there are no common factors among the terms, so we can't factor out any common factor.
Next, we can try factoring by grouping:
3x^3 + 2x - 8
= 3x^3 + 6x - 4x - 8
= 3x(x^2 + 2) - 4(x + 2)
= 3x(x^2 + 2) - 4(x^2 + 2)
= (3x - 4)(x^2 + 2)
So, the expression 3x^3 + 2x - 8 can be factored as (3x - 4)(x^2 + 2).
To factor the expression, we can look for common factors among the terms, and then see if any terms can be grouped together.
Factoring 3x^3 + 2x - 8:
First, note that there are no common factors among the terms, so we can't factor out any common factor.
Next, we can try factoring by grouping:
3x^3 + 2x - 8
= 3x^3 + 6x - 4x - 8
= 3x(x^2 + 2) - 4(x + 2)
= 3x(x^2 + 2) - 4(x^2 + 2)
= (3x - 4)(x^2 + 2)
So, the expression 3x^3 + 2x - 8 can be factored as (3x - 4)(x^2 + 2).
try resolving the equation with simplifying
To simplify further and possibly factor the expression 3x^3 + 2x - 8, we can try to find a common factor:
3x^3 + 2x - 8
The common factor among the terms is 1 (since there are no other numerical factors). We can rewrite the expression factoring out the common factor:
1(3x^3 + 2x - 8)
Now let's look at whether the expression 3x^3 + 2x - 8 can be simplified or factored:
There are no common factors to further simplify the expression. We can also determine that the expression cannot be factored further without using complex methods, as it does not seem to have any readily identifiable factors that would simplify it.
Therefore, the simplified expression for 3x^3 + 2x - 8 is 3x^3 + 2x - 8.
3x^3 + 2x - 8
The common factor among the terms is 1 (since there are no other numerical factors). We can rewrite the expression factoring out the common factor:
1(3x^3 + 2x - 8)
Now let's look at whether the expression 3x^3 + 2x - 8 can be simplified or factored:
There are no common factors to further simplify the expression. We can also determine that the expression cannot be factored further without using complex methods, as it does not seem to have any readily identifiable factors that would simplify it.
Therefore, the simplified expression for 3x^3 + 2x - 8 is 3x^3 + 2x - 8.