date: _______________ per: ______ unit 4: expressions & properties homework 6: the distributive property directions: simplify each expression using the distributive property. 1. 4(9 + 3) 2. 8(2 - 7) 3. -4(1 - 1 + 4) directions: simplify each expression using the distributive property. 4. 3(x + 5) 5. 7(w - 4) 6. -5(p + 2) 7. 4(8 - k) 8. 9(r + 7) 9. -12(m - 1) 10. 10(a + b) 11. -3(x - 2y) 12. -(4k + 1) 13. -9(2a - 5) 14. 5(3 - 2m) 15. $\frac{1}{5}(20m + 5)$ 16. $\frac{4}{3}(6v - 27)$ 17. 2(7m + 2n + 1) 18. -5(2a - b + 3) 19. if the figure below is a square, write an expression using parentheses to represent its perimeter. then, simplify the expression. $7x - 2$ square image 20. each day, elsa runs and walks the same number of minutes. if she runs for m minutes and walks for 5 minutes, write an expression using parentheses for the total number of minutes she will spend running and walking for 14 days. then, simplify the expression. review: simplify the expressions below by combining like terms. 21. 12n - 3 + 5n 22. 6w - 21 - w + 3 23. 1 + 14x - 16x + 14 24. -7r + r + 23 - 16 25. -41 - 2c + 13c - 7 26. 28 + 10p - 11p + 2 27. 9x - x + 4y - 23 - 15y 28. -2 - 13m - 4n - m + n + 7

Question

Accepted Answer

### Problem 1: $ 4(9 + 3) $
# Explanation:
## Step 1: Apply the distributive property $ a(b + c)=ab+ac $
$ 4\times9 + 4\times3 $
## Step 2: Calculate the products
$ 36+12 $
## Step 3: Add the results
$ 48 $
# Answer: $ 48 $

### Problem 2: $ 8(2 - 7) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ 8\times2-8\times7 $
## Step 2: Calculate the products
$ 16 - 56 $
## Step 3: Subtract the results
$ - 40 $
# Answer: $ -40 $

### Problem 3: $ - 4(1-1 + 4) $
# Explanation:
## Step 1: Simplify inside the parentheses
$ 1-1 + 4=4 $
## Step 2: Multiply by - 4
$ -4\times4=-16 $
# Answer: $ -16 $

### Problem 4: $ 3(x + 5) $
# Explanation:
## Step 1: Apply the distributive property $ a(b + c)=ab+ac $
$ 3\times x+3\times5 $
## Step 2: Simplify the products
$ 3x + 15 $
# Answer: $ 3x + 15 $

### Problem 5: $ 7(w - 4) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ 7\times w-7\times4 $
## Step 2: Simplify the products
$ 7w-28 $
# Answer: $ 7w - 28 $

### Problem 6: $ - 5(p + 2) $
# Explanation:
## Step 1: Apply the distributive property $ a(b + c)=ab+ac $
$ -5\times p+(-5)\times2 $
## Step 2: Simplify the products
$ -5p-10 $
# Answer: $ -5p - 10 $

### Problem 7: $ 4(8 - k) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ 4\times8-4\times k $
## Step 2: Simplify the products
$ 32-4k $
# Answer: $ 32 - 4k $

### Problem 8: $ 9(r + 7) $
# Explanation:
## Step 1: Apply the distributive property $ a(b + c)=ab+ac $
$ 9\times r+9\times7 $
## Step 2: Simplify the products
$ 9r + 63 $
# Answer: $ 9r + 63 $

### Problem 9: $ - 12(m - 1) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ -12\times m-(-12)\times1 $
## Step 2: Simplify the products
$ -12m + 12 $
# Answer: $ -12m + 12 $

### Problem 10: $ 10(a + b) $
# Explanation:
## Step 1: Apply the distributive property $ a(b + c)=ab+ac $
$ 10\times a+10\times b $
## Step 2: Simplify the products
$ 10a + 10b $
# Answer: $ 10a + 10b $

### Problem 11: $ - 3(x - 2y) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ -3\times x-(-3)\times2y $
## Step 2: Simplify the products
$ -3x + 6y $
# Answer: $ -3x + 6y $

### Problem 12: $ - (4k + 1) $
# Explanation:
## Step 1: Apply the distributive property $ -1\times(4k + 1)=-1\times4k+(-1)\times1 $
## Step 2: Simplify the products
$ -4k-1 $
# Answer: $ -4k - 1 $

### Problem 13: $ - 9(2a - 5) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ -9\times2a-(-9)\times5 $
## Step 2: Simplify the products
$ -18a + 45 $
# Answer: $ -18a + 45 $

### Problem 14: $ 5(3 - 2m) $
# Explanation:
## Step 1: Apply the distributive property $ a(b - c)=ab - ac $
$ 5\times3-5\times2m $
## Step 2: Simplify the products
$ 15-10m $
# Answer: $ 15 - 10m $

### Problem 15: $ \frac{1}{5}(20m + 5) $
# Explanation:
## Step 1: Apply the distributive property $ \frac{1}{5}\times20m+\frac{1}{5}\times5 $
## Step 2: Simplify the products
$ 4m + 1 $
# Answer: $ 4m + 1 $

### Problem 16: $ \frac{4}{3}(6v - 27) $
# Explanation:
## Step 1: Apply the distributive property $ \frac{4}{3}\times6v-\frac{4}{3}\times27 $
## Step 2: Simplify the products
$ 8v-36 $
# Answer: $ 8v - 36 $

### Problem 17: $ 2(7m + 2n + 1) $
# Explanation:
## Step 1: Apply the distributive property $ 2\times7m+2\times2n+2\times1 $
## Step 2: Simplify the products
$ 14m + 4n + 2 $
# Answer: $ 14m + 4n + 2 $

### Problem 18: $ - 5(2a - b + 3) $
# Explanation:
## Step 1: Apply the distributive property $ -5\times2a-(-5)\times b+(-5)\times3 $
## Step 2: Simplify the products
$ -10a + b-15 $
# Answer: $ -10a + b - 15 $

### Problem 19:
# Explanation:
## Step 1: Recall the perimeter of a square $ P = 4\times s $, where $ s $ is the side length. Here $ s=7x - 2 $, so the expression with parentheses is $ 4(7x - 2) $
## Step 2: Apply the distributive property $ 4\times7x-4\times2 $
## Step 3: Simplify the products
$ 28x-8 $
# Answer: The expression with parentheses is $ 4(7x - 2) $, and the simplified expression is $ 28x - 8 $

### Problem 20:
# Explanation:
## Step 1: Each day, the total minutes of running and walking is $ (m + 5) $. For 14 days, the expression with parentheses is $ 14(m + 5) $
## Step 2: Apply the distributive property $ 14\times m+14\times5 $
## Step 3: Simplify the products
$ 14m + 70 $
# Answer: The expression with parentheses is $ 14(m + 5) $, and the simplified expression is $ 14m + 70 $

### Problem 21: $ 12a-3 + 5a $
# Explanation:
## Step 1: Combine like terms (terms with $ a $): $ (12a + 5a)-3 $
## Step 2: Add the coefficients of $ a $
$ 17a-3 $
# Answer: $ 17a - 3 $

### Problem 22: $ 6w-21 - w+3 $
# Explanation:
## Step 1: Combine like terms: $ (6w - w)+(-21 + 3) $
## Step 2: Simplify each group
$ 5w-18 $
# Answer: $ 5w - 18 $

### Problem 23: $ 1 + 14x-16x + 14 $
# Explanation:
## Step 1: Combine like terms: $ (1 + 14)+(14x-16x) $
## Step 2: Simplify each group
$ 15-2x $
# Answer: $ 15 - 2x $

### Problem 24: $ - 7r+r + 23-16 $
# Explanation:
## Step 1: Combine like terms: $ (-7r + r)+(23 - 16) $
## Step 2: Simplify each group
$ -6r + 7 $
# Answer: $ -6r + 7 $

### Problem 25: $ - 41-2c + 13c-7 $
# Explanation:
## Step 1: Combine like terms: $ (-41 - 7)+(-2c + 13c) $
## Step 2: Simplify each group
$ -48 + 11c $ or $ 11c-48 $
# Answer: $ 11c - 48 $

### Problem 26: $ 28 + 10p-11p + 2 $
# Explanation:
## Step 1: Combine like terms: $ (28 + 2)+(10p-11p) $
## Step 2: Simplify each group
$ 30 - p $
# Answer: $ 30 - p $

### Problem 27: $ 9x-x + 4y-23-15y $
# Explanation:
## Step 1: Combine like terms: $ (9x - x)+(4y-15y)-23 $
## Step 2: Simplify each group
$ 8x-11y-23 $
# Answer: $ 8x - 11y - 23 $

### Problem 28: $ - 2-13m-4n-m + n+7 $
# Explanation:
## Step 1: Combine like terms: $ (-2 + 7)+(-13m - m)+(-4n + n) $
## Step 2: Simplify each group
$ 5-14m-3n $ or $ -14m-3n + 5 $
# Answer: $ -14m - 3n + 5 $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( 4(9 + 3) \)

Step 1: Apply the distributive property \( a(b + c)=ab+ac \)

Step 2: Calculate the products

Step 3: Add the results

Step 1: Apply the distributive property \( a(b - c)=ab - ac \)

Step 2: Calculate the products

Step 3: Subtract the results

Step 1: Simplify inside the parentheses

Step 2: Multiply by - 4

Answer:

Problem 2: \( 8(2 - 7) \)