Factor x^4-625

Problem

x4−625

Solution

1. Identify the expression as a difference of squares, since x4=(x2)2 and 625=25

2. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) where a=x2 and b=25

x4−625=(x2−25)*(x2+25)

3. Identify that the first factor, x2−25 is also a difference of squares because 25=5

4. Apply the formula again to the factor (x2−25)

x2−25=(x−5)*(x+5)

5. Combine all factors to write the completely factored expression.

(x−5)*(x+5)*(x2+25)

Final Answer

x4−625=(x−5)*(x+5)*(x2+25)

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