Ask AI: n⁴-49 factor

To factor \( n^4 - 49 \), you can recognize it as a difference of squares. The expression can be rewritten by expressing 49 as \( 7^2 \): \[ n^4 - 49 = n^4 - 7^2. \] Now apply the difference of squares formula, which states \( a^2 - b^2 = (a - b)(a + b) \): \[ n^4 - 7^2 = (n^2 - 7)(n^2 + 7). \] Neither \( n^2 - 7 \) nor \( n^2 + 7 \) can be factored further using real numbers since they are both irreducible quadratic expressions. Therefore, the fully factored form of \( n^4 - 49 \) over the reals is: \[ \boxed{(n^2 - 7)(n^2 + 7)}. \]