Factor 2x^4-162

Problem

2*x^4−162

Solution

1. Factor out the greatest common factor by dividing both terms by 2

2*(x^4−81)

2. Identify the difference of squares pattern, a^2−b^2=(a−b)*(a+b) where a=x^2 and b=9

2*((x^2)^2−9^2)

3. Apply the difference of squares formula to the expression inside the parentheses.

2*(x^2−9)*(x^2+9)

4. Identify another difference of squares in the factor (x^2−9) where a=x and b=3

2*(x^2−3^2)*(x^2+9)

5. Apply the difference of squares formula again to factor (x^2−9)

2*(x−3)*(x+3)*(x^2+9)

Final Answer

2*x^4−162=2*(x−3)*(x+3)*(x^2+9)

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