Factor a^4-b^4

Problem

a4−b4

Solution

1. Identify the expression as a difference of squares, noting that a4=(a2)2 and b4=(b2)2

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

a4−b4=(a2−b2)*(a2+b2)

3. Identify that the first factor, a2−b2 is also a difference of squares.

4. Factor the expression a2−b2 using the same formula.

a2−b2=(a−b)*(a+b)

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

(a−b)*(a+b)*(a2+b2)

Final Answer

a4−b4=(a−b)*(a+b)*(a2+b2)

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