Factor

Problem

5*(x2+3)4*(2*x)*(x−2)4+(x2+3)5*(4)*(x−2)3

Solution

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

2. Factor out the greatest common factor, which consists of (x2+3)4 (x−2)3 and the constant 2

3. Simplify the remaining expression inside the brackets by distributing and combining like terms.

4. Combine the factored terms into the final simplified form.

2*(x2+3)4*(x−2)3*[5*x*(x−2)+2*(x2+3)]

2*(x2+3)4*(x−2)3*[5*x2−10*x+2*x2+6]

2*(x2+3)4*(x−2)3*(7*x2−10*x+6)

Final Answer

5*(x2+3)4*(2*x)*(x−2)4+(x2+3)5*(4)*(x−2)3=2*(x2+3)4*(x−2)3*(7*x2−10*x+6)

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