(x2-4x%2B3)5dx.jpeg "(x-2)(x2-4x+3)5dx")
Evaluating the Expression: (x-2)(x²-4x+3)⁵ dx
In this article, we will explore the evaluation of the expression (x-2)(x²-4x+3)⁵ dx. This expression involves the product of two binomials raised to the power of 5, followed by the differential dx. To evaluate this expression, we will break it down into smaller parts and apply the correct mathematical operations.
Breaking Down the Expression
The given expression can be broken down into two parts:
(x-2): a binomial(x²-4x+3)⁵: a binomial raised to the power of 5
Evaluating the Binomials
Let's start by evaluating the first binomial:
(x-2) = x - 2
Now, let's focus on the second binomial:
(x²-4x+3)
To evaluate this binomial, we can start by expanding the square:
x² - 4x + 3 = x² - 4x + 4 - 1
= (x - 2)² - 1
Now, we can raise this expression to the power of 5:
((x-2)² - 1)⁵
= ((x-2)² - 1)((x-2)² - 1)((x-2)² - 1)((x-2)² - 1)((x-2)² - 1)
Multiplying the Binomials
Now that we have evaluated both binomials, we can multiply them together:
(x - 2)((x-2)² - 1)⁵
= (x³ - 2x² - x + 2)((x-2)² - 1)⁴
Evaluating the Differential
Finally, we need to evaluate the differential dx:
dx represents an infinitesimally small change in x
Final Expression
By combining all the above results, we can write the final expression as:
(x³ - 2x² - x + 2)((x-2)² - 1)⁴ dx
This is the evaluated expression for (x-2)(x²-4x+3)⁵ dx.
