Simplify

Problem

5*(x2+4)4*(2*x)*(x−2)4+(x2+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 (x2+4)4 (x−2)3 and the constant 2

2*(x2+4)4*(x−2)3*[5*x*(x−2)+2*(x2+4)]

3. Distribute the terms inside the square brackets.

2*(x2+4)4*(x−2)3*[5*x2−10*x+2*x2+8]

4. Combine like terms within the brackets.

2*(x2+4)4*(x−2)3*[7*x2−10*x+8]

Final Answer

5*(x2+4)4*(2*x)*(x−2)4+(x2+4)5*(4)*(x−2)3=2*(x2+4)4*(x−2)3*(7*x2−10*x+8)

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