4a^2-144b^2=(...)(...)

To factor the expression \(4a^2 - 144b^2\), we can start by recognizing that this is a difference of squares. The difference of squares can be expressed as \(A^2 - B^2 = (A - B)(A + B)\).

First, we can factor out the common factor from the expression:

\[ 4a^2 - 144b^2 = 4(a^2 - 36b^2) \]

Next, we notice that \(a^2 - 36b^2\) is also a difference of squares, since \(36b^2 = (6b)^2\). Thus, we can further factor this expression:

\[ a^2 - 36b^2 = (a - 6b)(a + 6b) \]

Putting it all together, we have:

\[ 4a^2 - 144b^2 = 4(a^2 - 36b^2) = 4(a - 6b)(a + 6b) \]

So the complete factorization of the expression \(4a^2 - 144b^2\) is:

\[ 4(a - 6b)(a + 6b) \]