Ask AI: a⁴-36 factor

To factor the expression \( a^4 - 36 \), you can use a combination of techniques including recognizing patterns and further factorization. 1. Recognize that \( a^4 - 36 \) is a difference of squares. This form is \( A^2 - B^2 \), which factors as \( (A + B)(A - B) \). Here, \( a^4 \) can be written as \( (a^2)^2 \), and 36 can be written as \( 6^2 \). So, you can write the expression as: \[ a^4 - 36 = (a^2)^2 - 6^2 \] 2. Apply the difference of squares formula: \[ (a^2)^2 - 6^2 = (a^2 + 6)(a^2 - 6) \] So, \( a^4 - 36 \) factors to \( (a^2 + 6)(a^2 - 6) \). 3. Check if the factors can be further factored: - \( a^2 + 6 \) cannot be factored further over the real numbers. - \( a^2 - 6 \) is also not a difference of squares or other common factorable form over the real numbers. Therefore, the fully factored form of \( a^4 - 36 \) is: \[ (a^2 + 6)(a^2 - 6) \]