Factor m^4-1

Problem

m^4−1

Solution

1. Identify the expression as a difference of squares, which follows the pattern a^2−b^2=(a−b)*(a+b)

2. Rewrite the terms as squares to match the pattern: (m^2)^2−(1)^2

3. Apply the formula for the difference of squares using a=m^2 and b=1

m^4−1=(m^2−1)*(m^2+1)

4. Identify that the first factor, m^2−1 is also a difference of squares.

5. Apply the formula again to the factor m^2−1 using a=m and b=1

m^2−1=(m−1)*(m+1)

6. Combine all factors to represent the fully factored form of the original expression.

Final Answer

m^4−1=(m−1)*(m+1)*(m^2+1)

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