Write as a polynomial. \[ \begin{array}{l}(x+3)(x+7)= \\ (x-2)(x+3)= \\ (2 a-3)(3 a-4)=\end{array} \]

Sure! Let's expand each of the given expressions into polynomial form. 1. **\((x + 3)(x + 7)\)** \[ \begin{align*} (x + 3)(x + 7) &= x \cdot x + x \cdot 7 + 3 \cdot x + 3 \cdot 7 \\ &= x^2 + 7x + 3x + 21 \\ &= x^2 + 10x + 21 \end{align*} \] 2. **\((x - 2)(x + 3)\)** \[ \begin{align*} (x - 2)(x + 3) &= x \cdot x + x \cdot 3 - 2 \cdot x - 2 \cdot 3 \\ &= x^2 + 3x - 2x - 6 \\ &= x^2 + x - 6 \end{align*} \] 3. **\((2a - 3)(3a - 4)\)** \[ \begin{align*} (2a - 3)(3a - 4) &= 2a \cdot 3a + 2a \cdot (-4) - 3 \cdot 3a - 3 \cdot (-4) \\ &= 6a^2 - 8a - 9a + 12 \\ &= 6a^2 - 17a + 12 \end{align*} \] --- **Final Expanded Polynomials:** \[ \begin{array}{l} (x + 3)(x + 7) = x^2 + 10x + 21 \\ (x - 2)(x + 3) = x^2 + x - 6 \\ (2a - 3)(3a - 4) = 6a^2 - 17a + 12 \end{array} \]