-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.