1. **State the problem:** Express the quadratic expression $16x^2 - 24x + 10$ in the form $(4x + a)^2 + b$. 2. **Recall the formula:** The expression $(4x + a)^2$ expands to $16x^2 + 8ax + a^2$. 3. **Match coefficients:** We want to find $a$ and $b$ such that: $$16x^2 - 24x + 10 = (4x + a)^2 + b = 16x^2 + 8ax + a^2 + b$$ 4. **Equate the coefficients of $x$:** $$8a = -24 \implies a = \frac{-24}{8} = -3$$ 5. **Substitute $a$ back and find $b$:** $$a^2 + b = 10 \implies (-3)^2 + b = 10 \implies 9 + b = 10 \implies b = 1$$ 6. **Write the final expression:** $$16x^2 - 24x + 10 = (4x - 3)^2 + 1$$ This is the expression in the desired form.