Factor x^4-36

Problem

x4−36

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 to determine the values of a and b

x4=(x2)2

36=6

3. Apply the formula for the difference of squares using a=x2 and b=6

(x2−6)*(x2+6)

4. Check if the resulting binomials can be factored further over the integers. Since neither 6 nor −6 are perfect squares, the expression is fully factored over the set of rational numbers.

Final Answer

x4−36=(x2−6)*(x2+6)

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