Factor x^4-625

Problem

x^4−625

Solution

1. Identify the expression as a difference of squares, since x^4=(x^2)^2 and 625=25^2

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

x^4−625=(x^2−25)*(x^2+25)

3. Identify that the first factor, x^2−25 is also a difference of squares because 25=5^2

4. Apply the formula again to the factor (x^2−25)

x^2−25=(x−5)*(x+5)

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

(x−5)*(x+5)*(x^2+25)

Final Answer

x^4−625=(x−5)*(x+5)*(x^2+25)

Want more problems? Check here!