Factor m^4-1

Problem

m4−1

Solution

1. Identify the expression as a difference of squares, which follows the pattern a2−b2=(a−b)*(a+b)

2. Rewrite the terms as squares to match the pattern: (m2)2−(1)2

3. Apply the formula for the difference of squares using a=m2 and b=1

m4−1=(m2−1)*(m2+1)

4. Identify that the first factor, m2−1 is also a difference of squares.

5. Apply the formula again to the factor m2−1 using a=m and b=1

m2−1=(m−1)*(m+1)

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

Final Answer

m4−1=(m−1)*(m+1)*(m2+1)

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