To express \(16x^2 - 24x + 10\) in the form \((4x + a)^2 + b\), follow these steps:

1.

Start by expanding \((4x + a)^2\):

\((4x + a)^2 = 16x^2 + 8ax + a^2\) 2.

Compare coefficients with \(16x^2 - 24x + 10\):

- The coefficient of \(x\) gives: \(8a = -24\) - Solve for \(a\):

\(a = \frac{-24}{8} = -3\) 3.

Substitute \(a = -3\) back into \((4x + a)^2\):

\((4x - 3)^2 = 16x^2 - 24x + 9\) 4.

Find \(b\) by comparing the constant terms:

\(16x^2 - 24x + 10 = (4x - 3)^2 + b\) - From \(9 + b = 10\), solve for \(b\):

\(b = 1\) 5.

Thus, the expression is:

\((4x - 3)^2 + 1\)