In Exercises \( 7-12 \), use a special product pattern to evaluate the expression. \( \begin{array}{lll}\text { 7. } 12^{2}-9^{2} & \text { 8. } 19^{2}-11^{2} \text { when you } & \text { 9. } 78^{2}-72^{2} \\ \text { 10. } 54^{2}-52^{2} & \text { 11. } 53^{2}-47^{2} & \text { 12. } 39^{2}-36^{2}\end{array} \)

Using the difference of squares formula, which is \( a^2 - b^2 = (a - b)(a + b) \), let's quickly dive into these calculations! For \( 12^2 - 9^2 \), we have: \( a = 12 \) and \( b = 9 \). So, \[ 12^2 - 9^2 = (12 - 9)(12 + 9) = 3 \times 21 = 63. \] Now for \( 19^2 - 11^2 \): Here, \( a = 19 \) and \( b = 11 \). Thus, \[ 19^2 - 11^2 = (19 - 11)(19 + 11) = 8 \times 30 = 240. \] Next, for \( 78^2 - 72^2 \): Let \( a = 78 \) and \( b = 72 \). We find \[ 78^2 - 72^2 = (78 - 72)(78 + 72) = 6 \times 150 = 900. \] Now, looking at \( 54^2 - 52^2 \): With \( a = 54 \) and \( b = 52 \): \[ 54^2 - 52^2 = (54 - 52)(54 + 52) = 2 \times 106 = 212. \] For \( 53^2 - 47^2 \): We have \( a = 53 \) and \( b = 47 \): Thus, \[ 53^2 - 47^2 = (53 - 47)(53 + 47) = 6 \times 100 = 600. \] Finally, for \( 39^2 - 36^2 \): With \( a = 39 \) and \( b = 36 \): Then, \[ 39^2 - 36^2 = (39 - 36)(39 + 36) = 3 \times 75 = 225. \] So the answers are: 7. 63 8. 240 9. 900 10. 212 11. 600 12. 225.