Factor 81x^4-16

Problem

81*x4−16

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.

81*x4=(9*x2)2

16=4

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

81*x4−16=(9*x2−4)*(9*x2+4)

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

9*x2=(3*x)2

4=2

5. Apply the formula again to factor (9*x2−4)

9*x2−4=(3*x−2)*(3*x+2)

6. Combine all factors to write the final factored form.

81*x4−16=(3*x−2)*(3*x+2)*(9*x2+4)

Final Answer

81*x4−16=(3*x−2)*(3*x+2)*(9*x2+4)

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