To express \(4x^2 - 12x + 13\) in the form \((2x + a)^2 + b\), we start by expanding \((2x + a)^2\):

\((2x + a)^2 = (2x)^2 + 2 \cdot 2x \cdot a + a^2 = 4x^2 + 4ax + a^2\).

We want this to match \(4x^2 - 12x + 13\). Comparing coefficients, we have:

\(4ax = -12x\) implies \(4a = -12\), so \(a = -3\).

Substitute \(a = -3\) into \(a^2\):

\(a^2 = (-3)^2 = 9\).

Now, compare the constant terms:

\(a^2 + b = 13\) implies \(9 + b = 13\), so \(b = 4\).

Thus, the expression is \((2x - 3)^2 + 4\).