Simplify

Problem

5*(x^2+4)^4*(2*x)*(x−2)^4+(x^2+4)^5*(4)*(x−2)^3

Solution

1. Identify the common factors in both terms of the expression.

2. Factor out the greatest common factors, which are (x^2+4)^4 (x−2)^3 and the constant 2

2*(x^2+4)^4*(x−2)^3*[5*x*(x−2)+2*(x^2+4)]

3. Distribute the terms inside the square brackets.

2*(x^2+4)^4*(x−2)^3*[5*x^2−10*x+2*x^2+8]

4. Combine like terms within the brackets.

2*(x^2+4)^4*(x−2)^3*[7*x^2−10*x+8]

Final Answer

5*(x^2+4)^4*(2*x)*(x−2)^4+(x^2+4)^5*(4)*(x−2)^3=2*(x^2+4)^4*(x−2)^3*(7*x^2−10*x+8)

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