Factor a^4-b^4

Problem

a^4−b^4

Solution

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

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

a^4−b^4=(a^2−b^2)*(a^2+b^2)

3. Identify that the first factor, a^2−b^2 is also a difference of squares.

4. Factor the expression a^2−b^2 using the same formula.

a^2−b^2=(a−b)*(a+b)

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

(a−b)*(a+b)*(a^2+b^2)

Final Answer

a^4−b^4=(a−b)*(a+b)*(a^2+b^2)

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