Question

foundations 2
distributive property quiz review
simplify each expression.

1. 3(x + 3)
2. 2(n + 6)
3. 5(2 + x)
4. 8(n + 6)
5. 4(m + 1)
6. 8(k + 5)
7. -(x + 5)
8. 3(k - 8)
9. -5(v + 6)
10. 3(1 - b)
11. -8(n - 2)
12. -5(v + 1)
13. 8(r - 5)
14. -5(a - 8)

Explanation:

Step1: Simplify \(3(x + 3)\)

Using the distributive property \(a(b + c)=ab+ac\), here \(a = 3\), \(b=x\), \(c = 3\). So \(3\times x+3\times3=3x + 9\).

Step2: Simplify \(2(n + 6)\)

Using the distributive property, \(a = 2\), \(b=n\), \(c = 6\). So \(2\times n+2\times6=2n+12\).

Step3: Simplify \(5(2 + x)\)

Using the distributive property, \(a = 5\), \(b = 2\), \(c=x\). So \(5\times2+5\times x=10 + 5x\).

Step4: Simplify \(8(n + 6)\)

Using the distributive property, \(a = 8\), \(b=n\), \(c = 6\). So \(8\times n+8\times6=8n + 48\).

Step5: Simplify \(4(m + 1)\)

Using the distributive property, \(a = 4\), \(b=m\), \(c = 1\). So \(4\times m+4\times1=4m+4\).

Step6: Simplify \(8(k + 5)\)

Using the distributive property, \(a = 8\), \(b=k\), \(c = 5\). So \(8\times k+8\times5=8k + 40\).

Step7: Simplify \(-(x + 5)\)

Using the distributive property, \(a=- 1\), \(b=x\), \(c = 5\). So \(-1\times x+(-1)\times5=-x - 5\) (the original answer here is wrong, correct is \(-x - 5\)).

Step8: Simplify \(3(k - 8)\)

Using the distributive property \(a(b - c)=ab - ac\), here \(a = 3\), \(b=k\), \(c = 8\). So \(3\times k-3\times8=3k-24\) (the original answer here is wrong, correct is \(3k - 24\)).

Step9: Simplify \(-5(v + 6)\)

Using the distributive property, \(a=-5\), \(b = v\), \(c = 6\). So \(-5\times v+(-5)\times6=-5v-30\).

Step10: Simplify \(3(1 - b)\)

Using the distributive property \(a(b - c)=ab - ac\), here \(a = 3\), \(b = 1\), \(c=b\). So \(3\times1-3\times b=3-3b\) (the original answer here is wrong, correct is \(3 - 3b\)).

Step11: Simplify \(-8(n - 2)\)

Using the distributive property \(a(b - c)=ab - ac\), here \(a=-8\), \(b=n\), \(c = 2\). So \(-8\times n-(-8)\times2=-8n + 16\) (the original answer is missing, correct is \(-8n + 16\)).

Step12: Simplify \(-5(v + 1)\)

Using the distributive property, \(a=-5\), \(b = v\), \(c = 1\). So \(-5\times v+(-5)\times1=-5v-5\) (the original answer is missing, correct is \(-5v - 5\)).

Step13: Simplify \(8(r - 5)\)

Using the distributive property \(a(b - c)=ab - ac\), here \(a = 8\), \(b=r\), \(c = 5\). So \(8\times r-8\times5=8r-40\) (the original answer is missing, correct is \(8r - 40\)).

Step14: Simplify \(-5(a - 8)\)

Using the distributive property \(a(b - c)=ab - ac\), here \(a=-5\), \(b=a\), \(c = 8\). So \(-5\times a-(-5)\times8=-5a + 40\) (the original answer is missing, correct is \(-5a + 40\)).

Answer:

1. \(3x + 9\)
2. \(2n + 12\)
3. \(10 + 5x\)
4. \(8n + 48\)
5. \(4m + 4\)
6. \(8k + 40\)
7. \(-x - 5\) (corrected)
8. \(3k - 24\) (corrected)
9. \(-5v - 30\)
10. \(3 - 3b\) (corrected)
11. \(-8n + 16\) (corrected)
12. \(-5v - 5\) (corrected)
13. \(8r - 40\) (corrected)
14. \(-5a + 40\) (corrected)