-49a^2+16b^2

The expression \(-49a^2 + 16b^2\) can be recognized as a difference of squares, which can be factored using the difference of squares formula: \[ x^2 - y^2 = (x - y)(x + y) \] To apply this formula, we rewrite the expression: \[ -49a^2 + 16b^2 = 16b^2 - 49a^2 \] Now we can identify \(x\) and \(y\): - \(x = 4b\) (since \((4b)^2 = 16b^2\)) - \(y = 7a\) (since \((7a)^2 = 49a^2\)) Now, substitute \(x\) and \(y\) into the difference of squares formula: \[ 16b^2 - 49a^2 = (4b - 7a)(4b + 7a) \] Thus, the factored form of \(-49a^2 + 16b^2\) is: \[ -(7a - 4b)(7a + 4b) \] Alternatively, you could express it as: \[ -(4b - 7a)(4b + 7a) \] Either way, the factored form captures the original expression.