1. We are given the quadratic expression $16x^2 - 24x + 10$ and want to express it in the form $(4x + a)^2 + b$. 2. Recall the formula for expanding a binomial square: $$(4x + a)^2 = (4x)^2 + 2 \cdot 4x \cdot a + a^2 = 16x^2 + 8ax + a^2.$$ 3. We want to match this to $16x^2 - 24x + 10$. Equate the coefficients of like terms: - Coefficient of $x^2$: $16 = 16$ (already matches) - Coefficient of $x$: $8a = -24 \implies a = \frac{-24}{8} = -3$ - Constant term: $a^2 + b = 10 \implies (-3)^2 + b = 10 \implies 9 + b = 10 \implies b = 1$ 4. Therefore, the expression can be rewritten as: $$16x^2 - 24x + 10 = (4x - 3)^2 + 1.$$