Factor 256x^4-81

Problem

256*x4−81

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 of simpler expressions.

256*x4=(16*x2)2

81=9

3. Apply the formula for the difference of squares to the initial expression.

256*x4−81=(16*x2−9)*(16*x2+9)

4. Identify that the first factor (16*x2−9) is also a difference of squares.

16*x2=(4*x)2

9=3

5. Apply the formula again to the factor (16*x2−9)

16*x2−9=(4*x−3)*(4*x+3)

6. Combine all factors into the final expression, noting that the sum of squares (16*x2+9) cannot be factored further using real numbers.

Final Answer

256*x4−81=(4*x−3)*(4*x+3)*(16*x2+9)

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