Simplify (2x(x+6)^4-x^2*4(x+6)^3)/((x+6)^8)

Problem

(2*x*(x+6)4−x2⋅4*(x+6)3)/((x+6)8)

Solution

1. Identify the common factor in the numerator. Both terms contain 2*x and (x+6)3

2. Factor out the greatest common factor 2*x*(x+6)3 from the numerator.

2*x*(x+6)3*[(x+6)−2*x]

3. Simplify the expression inside the brackets by combining like terms.

(x+6)−2*x=6−x

4. Rewrite the numerator with the simplified bracket.

2*x*(x+6)3*(6−x)

5. Divide the numerator and the denominator by the common factor (x+6)3

(2*x*(x+6)3*(6−x))/((x+6)8)=(2*x*(6−x))/((x+6)5)

6. Distribute the 2*x in the numerator to reach the final simplified form.

2*x*(6−x)=12*x−2*x2

Final Answer

(2*x*(x+6)4−x2⋅4*(x+6)3)/((x+6)8)=(12*x−2*x2)/((x+6)5)

Want more problems? Check here!