Factor x^6-y^6

Problem

x6−y6

Solution

1. Identify the expression as a difference of squares, since x6=(x3)2 and y6=(y3)2

2. Apply the difference of squares formula, a2−b2=(a−b)*(a+b) where a=x3 and b=y3

x6−y6=(x3−y3)*(x3+y3)

3. Factor the first term using the difference of cubes formula, a3−b3=(a−b)*(a2+a*b+b2)

x3−y3=(x−y)*(x2+x*y+y2)

4. Factor the second term using the sum of cubes formula, a3+b3=(a+b)*(a2−a*b+b2)

x3+y3=(x+y)*(x2−x*y+y2)

5. Combine all the factors into a single expression.

(x−y)*(x2+x*y+y2)*(x+y)*(x2−x*y+y2)

Final Answer

x6−y6=(x−y)*(x+y)*(x2+x*y+y2)*(x2−x*y+y2)

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