Factor by removing the common factor with the lesser exponent
2x(x-5)^-3 -4x^2(x-5)^-4
I don't really know how to do this.
The final answer I got is:
2x(2x^2-10x+1)
--------------
(x-5)^4
2x(x-5)^-3(1-2x(x-5)^-1) =
2x/(x-5)^3 * (1-2x/(x-5)) =
2x/(x-5)^3 * ((x-5)/(x-5)-2x/(x-5) =
2x/(x-5)^3 * (-x-5)/(x-5) =
2x(-x-5))/(x-5)^4).
Take a look at what wolframalpha got:
http://www.wolframalpha.com/input/?i=2x+%28x-5%29^-3+-4x^2+%28x-5%29^-4
To factor the given expression by removing the common factor with the lesser exponent, follow these steps:
1. Identify the common factor between the two terms:
The common factor in this case is (x-5)^-3 since it appears in both terms.
2. Determine the lesser exponent of the common factor:
Compare the exponents of (x-5) in each term: -3 and -4. The lesser exponent is -4.
3. Remove the common factor with the lesser exponent:
To remove the common factor (x-5)^-4, divide each term by (x-5)^-4:
(2x(x-5)^-3) / (x-5)^-4 - (4x^2(x-5)^-4) / (x-5)^-4
This simplifies to:
2x(x-5)^1 - 4x^2(x-5)^0
Now, simplify further:
2x(x-5) - 4x^2
4. Combine like terms, if possible:
In this case, there are no like terms that can be combined.
So, the final factored expression is:
2x(x-5) - 4x^2