Factor 16x^4-81

Problem

16*x4−81

Solution

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

2. Rewrite the terms as squares of simpler expressions.

16*x4=(4*x2)2

81=9

3. Apply the formula for the difference of squares using a=4*x2 and b=9

16*x4−81=(4*x2−9)*(4*x2+9)

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

4*x2=(2*x)2

9=3

5. Apply the formula again to the factor (4*x2−9) using a=2*x and b=3

4*x2−9=(2*x−3)*(2*x+3)

6. Combine all factors into the final expression. Note that 4*x2+9 is a sum of squares and cannot be factored further using real numbers.

Final Answer

16*x4−81=(2*x−3)*(2*x+3)*(4*x2+9)

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