Factor 81x^4-256

Problem

81*x^4−256

Solution

1. Identify the expression as a difference of squares, since both terms are perfect squares.

2. Apply the formula for the difference of squares, a^2−b^2=(a−b)*(a+b) where a=9*x^2 and b=16

81*x^4−256=(9*x^2−16)*(9*x^2+16)

3. Identify that the first factor, 9*x^2−16 is also a difference of squares where a=3*x and b=4

4. Factor the expression 9*x^2−16 using the difference of squares formula.

9*x^2−16=(3*x−4)*(3*x+4)

5. Combine all factors to write the completely factored form of the original expression.

81*x^4−256=(3*x−4)*(3*x+4)*(9*x^2+16)

Final Answer

81*x^4−256=(3*x−4)*(3*x+4)*(9*x^2+16)

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