Factor 16x^4-1

Problem

16*x4−1

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 find a and b

16*x4=(4*x2)2

1=(1)2

3. Apply the formula for the difference of squares using a=4*x2 and b=1

16*x4−1=(4*x2−1)*(4*x2+1)

4. Identify that the first factor (4*x2−1) is also a difference of squares.

5. Rewrite the terms of the first factor as squares.

4*x2=(2*x)2

1=(1)2

6. Apply the formula again to the factor (4*x2−1) using a=2*x and b=1

4*x2−1=(2*x−1)*(2*x+1)

7. Combine all factors into the final expression.

Final Answer

16*x4−1=(2*x−1)*(2*x+1)*(4*x2+1)

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