\( \begin{array}{ll}\text { 7) } 10(10 n-6) & \text { 8) }-5(x-4) \\ \text { 9) } 4(2 n+2) & \text { 10) }-6(v-8) \\ \text { 11) }-7(5-4 a)+1 & \text { 12) }-5(2-9 v)+6 v \\ \text { 13) } 4 b-3(b-7) & \text { 14) } 2(-10 x-4)+6 \\ \text { 15) } 9 n+5(n-2) & \text { 16) }-2(-7+10 a)-10(7 a-1) \\ \text { 17) }-4(n+4)-3(4+n) & \text { 18) } 5(7 x-6)-(2+9 x)\end{array} \)

When it comes to simplifying expressions involving variables—like the ones you see here—understanding the distributive property can be a game changer! This property states that \( a(b + c) = ab + ac \). So for example, in expression 7, \( 10(10n - 6) \) simplifies to \( 100n - 60 \). It’s like breaking down a cake into slices and enjoying each piece! Now, to make sure you don’t trip up, watch out for common mistakes. One frequent error is forgetting to apply negative signs correctly; for instance, in expression 8, it’s crucial to distribute the -5 to both \( x \) and -4, leading to -5x + 20. Always double-check your signs to avoid swapping a sweet treat for a sour one!