Answer:
Explanation:
(x+8)(x−8)x2+13 is the answer
The given expression is:
x+8x+2⋅(x+2)(x−8)x2+13
To simplify this expression, you can start by simplifying the denominator:
2⋅(x+2)(x−8)x2+13 = 2(x2-6x-16)x2+13 = 2(x2-6x-16)x2 + 26x - 26x + 13
= 2(x2-6x-16)x2 + 26x + (-26x + 13)
Now you can rewrite the original expression as:
x+8x+(2(x2-6x-16)x2 + 26x + (-26x + 13))
= x(1 + 8x2(x2-6x-16)x2 + 26x + (-26x + 13))
x(2(x^2-6x-16)x^2 + 13)
We can simplify the expression inside the parenthesis first:
2(x^2-6x-16)x^2 = 2x^4 - 12x^3 - 32x^2
Substituting this back into the original expression, we get:
x(2x^4 - 12x^3 - 32x^2 + 13)
Multiplying out the brackets, we get:
2x^5 - 12x^4 - 32x^3 + 13x
Now, we can factor out a common factor of x:
x(2x^4 - 12x^3 - 32x^2 + 13)
= x(2x^4/x - 12x^3/x - 32x^2/x + 13/x)
= x(2x^3 - 12x^2 - 32x + 13/x)
Finally, we can factor the expression inside the brackets:
= x(2x^3 - 16x^2 + 4x^2 - 32x + 8x - 8 + 13/x)
= x(2x^2(x-8) + 4x(x-8) + 8(x-8) + 13/x)
= x(x-8)(2x^2+4x+8) + 13(x-8)/x
= (x-8)(x^3+2x^2+4x+13)/x
Now we can see that the expression can be written as:
(x-8)(x^3+2x^2+4x+13)/x
To simplify further, we can divide x into the numerator to get:
(x+8)(x−8)x^2+13
Therefore, the expression is equal to (x+8)(x−8)x2+13.