QuestionAugust 26, 2025

2) 5(-3p-10)+10 4) 10m(8m+1)-3m 6) 9m-4(5-3m) 8) -7n-10(n-4) 10) 10(b+7)+5b(b-7) 12) 10(v+5)+9(v-8)

2) 5(-3p-10)+10 4) 10m(8m+1)-3m 6) 9m-4(5-3m) 8) -7n-10(n-4) 10) 10(b+7)+5b(b-7) 12) 10(v+5)+9(v-8)
2) 5(-3p-10)+10 4) 10m(8m+1)-3m 6) 9m-4(5-3m) 8) -7n-10(n-4) 10) 10(b+7)+5b(b-7) 12) 10(v+5)+9(v-8)

Solution
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Answer

2) -15p - 40 ### 4) 80m^2 + 7m ### 6) 21m - 20 ### 8) -17n + 40 ### 10) 5b^2 - 25b + 70 ### 12) 19v - 22 Explanation 1. Simplify Expression 2 Distribute 5 in 5(-3p-10): 5 \cdot (-3p) + 5 \cdot (-10) = -15p - 50. Add 10: -15p - 50 + 10 = -15p - 40. 2. Simplify Expression 4 Distribute 10m in 10m(8m+1): 10m \cdot 8m + 10m \cdot 1 = 80m^2 + 10m. Subtract 3m: 80m^2 + 10m - 3m = 80m^2 + 7m. 3. Simplify Expression 6 Distribute -4 in -4(5-3m): -4 \cdot 5 + (-4) \cdot (-3m) = -20 + 12m. Combine with 9m: 9m + 12m - 20 = 21m - 20. 4. Simplify Expression 8 Distribute -10 in -10(n-4): -10 \cdot n + (-10) \cdot (-4) = -10n + 40. Combine with -7n: -7n - 10n + 40 = -17n + 40. 5. Simplify Expression 10 Distribute 10 in 10(b+7): 10b + 70. Distribute 5b in 5b(b-7): 5b^2 - 35b. Combine: 10b + 70 + 5b^2 - 35b = 5b^2 - 25b + 70. 6. Simplify Expression 12 Distribute 10 in 10(v+5): 10v + 50. Distribute 9 in 9(v-8): 9v - 72. Combine: 10v + 50 + 9v - 72 = 19v - 22.

Explanation

1. Simplify Expression 2<br /> Distribute $5$ in $5(-3p-10)$: $5 \cdot (-3p) + 5 \cdot (-10) = -15p - 50$. Add $10$: $-15p - 50 + 10 = -15p - 40$.<br /><br />2. Simplify Expression 4<br /> Distribute $10m$ in $10m(8m+1)$: $10m \cdot 8m + 10m \cdot 1 = 80m^2 + 10m$. Subtract $3m$: $80m^2 + 10m - 3m = 80m^2 + 7m$.<br /><br />3. Simplify Expression 6<br /> Distribute $-4$ in $-4(5-3m)$: $-4 \cdot 5 + (-4) \cdot (-3m) = -20 + 12m$. Combine with $9m$: $9m + 12m - 20 = 21m - 20$.<br /><br />4. Simplify Expression 8<br /> Distribute $-10$ in $-10(n-4)$: $-10 \cdot n + (-10) \cdot (-4) = -10n + 40$. Combine with $-7n$: $-7n - 10n + 40 = -17n + 40$.<br /><br />5. Simplify Expression 10<br /> Distribute $10$ in $10(b+7)$: $10b + 70$. Distribute $5b$ in $5b(b-7)$: $5b^2 - 35b$. Combine: $10b + 70 + 5b^2 - 35b = 5b^2 - 25b + 70$.<br /><br />6. Simplify Expression 12<br /> Distribute $10$ in $10(v+5)$: $10v + 50$. Distribute $9$ in $9(v-8)$: $9v - 72$. Combine: $10v + 50 + 9v - 72 = 19v - 22$.
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