Factor x^4-8x^2+16

Problem

x4−8*x2+16

Solution

1. Identify the expression as a trinomial in the form of a perfect square, specifically a2−2*a*b+b2

2. Determine the square roots of the first and last terms, where a=√(,x4)=x2 and b=√(,16)=4

3. Verify the middle term by calculating 2*a*b=2*(x2)*(4)=8*x2 which matches the given expression.

4. Apply the perfect square trinomial formula (a−b)2 to get (x2−4)2

5. Recognize that the inner expression x2−4 is a difference of squares, which factors into (x−2)*(x+2)

6. Substitute this factorization back into the squared expression to get ((x−2)*(x+2))2

7. Distribute the exponent to each factor.

Final Answer

x4−8*x2+16=(x−2)2*(x+2)2

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