Factor x^4-81

Problem

x^4−81

Solution

1. Identify the expression as a difference of squares, since x^4=(x^2)^2 and 81=9^2

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

x^4−81=(x^2−9)*(x^2+9)

3. Identify that the first factor, x^2−9 is also a difference of squares because 9=3^2

4. Apply the formula again to the factor (x^2−9)

x^2−9=(x−3)*(x+3)

5. Combine all factors into the final expression. Note that x^2+9 is a sum of squares and cannot be factored further using real numbers.

(x−3)*(x+3)*(x^2+9)

Final Answer

x^4−81=(x−3)*(x+3)*(x^2+9)

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