Question

distributive property

1. -6(a + 8) =
2. 4(1 + 9a) =
3. 6(-5a + 7) =
4. (9a + 10) * 2 =
5. (-4 - 3a) * -8 =
6. 8(-a - 4) =
7. (1 - 7n) * 5 =
8. -6(n + 4) =
9. 5(3n - 6) =
10. (-6n + 7) * -4 =
11. 5(n - 1) =
12. (n + 9) * 5 =

5n - 5 -30a + 42 5 - 35n 24n - 28 -8a - 32 -6a - 48
18a + 20 4 + 36a 32 + 24a 15n - 30 5n + 45 -6n - 24

Explanation:

Step1: Apply distributive property

For \(-6(a + 8)\), we multiply -6 by each term inside the parentheses: \(-6\times a+(-6)\times8=-6a - 48\).

Step2: Apply distributive property

For \(4(1 + 9a)\), we have \(4\times1+4\times9a = 4+36a\).

Step3: Apply distributive property

For \(6(-5a + 7)\), we get \(6\times(-5a)+6\times7=-30a + 42\).

Step4: Apply distributive property

For \((9a + 10)\times2\), it is \(9a\times2+10\times2 = 18a+20\).

Step5: Apply distributive property

For \((-4 - 3a)\times(-8)\), we calculate \((-4)\times(-8)+(-3a)\times(-8)=32 + 24a\).

Step6: Apply distributive property

For \(8(-a - 4)\), we have \(8\times(-a)+8\times(-4)=-8a - 32\).

Step7: Apply distributive property

For \((1 - 7n)\times5\), it is \(1\times5-7n\times5 = 5-35n\).

Step8: Apply distributive property

For \(-6(n + 4)\), we get \(-6\times n+(-6)\times4=-6n - 24\).

Step9: Apply distributive property

For \(5(3n - 6)\), we calculate \(5\times3n-5\times6 = 15n-30\).

Step10: Apply distributive property

For \((-6n + 7)\times(-4)\), we have \((-6n)\times(-4)+7\times(-4)=24n - 28\).

Step11: Apply distributive property

For \(5(n - 1)\), it is \(5\times n-5\times1 = 5n-5\).

Step12: Apply distributive property

For \((n + 9)\times5\), we get \(n\times5+9\times5 = 5n + 45\).

Answer:

1. \(-6a - 48\)
2. \(4 + 36a\)
3. \(-30a + 42\)
4. \(18a+20\)
5. \(32 + 24a\)
6. \(-8a - 32\)
7. \(5-35n\)
8. \(-6n - 24\)
9. \(15n-30\)
10. \(24n - 28\)
11. \(5n-5\)
12. \(5n + 45\)