Factor x^4-y^4

Problem

x4−y4

Solution

1. Identify the expression as a difference of squares, noting that x4=(x2)2 and y4=(y2)2

2. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) where a=x2 and b=y2

x4−y4=(x2−y2)*(x2+y2)

3. Identify that the first factor, (x2−y2) is also a difference of squares.

4. Apply the formula again to the factor (x2−y2)

x2−y2=(x−y)*(x+y)

5. Combine all factors into the final expression.

(x−y)*(x+y)*(x2+y2)

Final Answer

x4−y4=(x−y)*(x+y)*(x2+y2)

Want more problems? Check here!