Factor 16x^4-81y^4

Problem

16*x4−81*y4

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 perfect squares.

16*x4=(4*x2)2

81*y4=(9*y2)2

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

16*x4−81*y4=(4*x2−9*y2)*(4*x2+9*y2)

4. Identify that the first factor (4*x2−9*y2) is also a difference of squares.

4*x2=(2*x)2

9*y2=(3*y)2

5. Factor the term (4*x2−9*y2) using the difference of squares formula again.

4*x2−9*y2=(2*x−3*y)*(2*x+3*y)

6. Combine all factors into the final expression. Note that (4*x2+9*y2) is a sum of squares and cannot be factored further using real coefficients.

Final Answer

16*x4−81*y4=(2*x−3*y)*(2*x+3*y)*(4*x2+9*y2)

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