Factor x^4-y^4

Problem

x^4−y^4

Solution

1. Identify the expression as a difference of squares, noting that x^4=(x^2)^2 and y^4=(y^2)^2

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

x^4−y^4=(x^2−y^2)*(x^2+y^2)

3. Identify that the first factor, (x^2−y^2) is also a difference of squares.

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

x^2−y^2=(x−y)*(x+y)

5. Combine all factors into the final expression.

(x−y)*(x+y)*(x^2+y^2)

Final Answer

x^4−y^4=(x−y)*(x+y)*(x^2+y^2)

Want more problems? Check here!