Distributive Property Worksheet for simplifying algebraic expressions.

Here are the step-by-step solutions for each problem on the worksheet.

1.) $5(c + 4)$
* Multiply 5 by $c$: $5 \cdot c = 5c$
* Multiply 5 by 4: $5 \cdot 4 = 20$
* Combine them: $5c + 20$

2.) $10(y - 3)$
* Multiply 10 by $y$: $10 \cdot y = 10y$
* Multiply 10 by -3: $10 \cdot -3 = -30$
* Combine them: $10y - 30$

3.) $4(2a + 5b)$
* Multiply 4 by $2a$: $4 \cdot 2a = 8a$
* Multiply 4 by $5b$: $4 \cdot 5b = 20b$
* Combine them: $8a + 20b$

4.) $3(2c + 2a + 3b)$
* Multiply 3 by $2c$: $3 \cdot 2c = 6c$
* Multiply 3 by $2a$: $3 \cdot 2a = 6a$
* Multiply 3 by $3b$: $3 \cdot 3b = 9b$
* Combine them: $6c + 6a + 9b$

5.) $6(x + 5) + 11x$
* First, distribute the 6 into the parentheses: $6 \cdot x = 6x$ and $6 \cdot 5 = 30$. So, we have $6x + 30$.
* Now add the remaining term: $6x + 30 + 11x$.
* Combine like terms ($6x$ and $11x$): $6x + 11x = 17x$.
* Final expression: $17x + 30$

6.) $10(x + 2) - 3$
* Distribute the 10: $10 \cdot x = 10x$ and $10 \cdot 2 = 20$. So, we have $10x + 20$.
* Subtract 3: $10x + 20 - 3$.
* Combine constants ($20 - 3$): $17$.
* Final expression: $10x + 17$

7.) $(5 + t)5 + 20t$
* Distribute the 5 to both terms inside the parentheses: $5 \cdot 5 = 25$ and $t \cdot 5 = 5t$. So, we have $25 + 5t$.
* Add the remaining term: $25 + 5t + 20t$.
* Combine like terms ($5t$ and $20t$): $5t + 20t = 25t$.
* Final expression: $25 + 25t$ (or $25t + 25$)

8.) $7(q + m) + 3q - 2m$
* Distribute the 7: $7 \cdot q = 7q$ and $7 \cdot m = 7m$. So, we have $7q + 7m$.
* Add the remaining terms: $7q + 7m + 3q - 2m$.
* Combine $q$ terms: $7q + 3q = 10q$.
* Combine $m$ terms: $7m - 2m = 5m$.
* Final expression: $10q + 5m$

9.) $2(m + 4) + 3(m + 8)$
* Distribute the 2: $2 \cdot m = 2m$ and $2 \cdot 4 = 8$. Result: $2m + 8$.
* Distribute the 3: $3 \cdot m = 3m$ and $3 \cdot 8 = 24$. Result: $3m + 24$.
* Put it all together: $2m + 8 + 3m + 24$.
* Combine $m$ terms: $2m + 3m = 5m$.
* Combine numbers: $8 + 24 = 32$.
* Final expression: $5m + 32$

10.) $9(b - 4) + 6(b + 6)$
* Distribute the 9: $9 \cdot b = 9b$ and $9 \cdot -4 = -36$. Result: $9b - 36$.
* Distribute the 6: $6 \cdot b = 6b$ and $6 \cdot 6 = 36$. Result: $6b + 36$.
* Put it all together: $9b - 36 + 6b + 36$.
* Combine $b$ terms: $9b + 6b = 15b$.
* Combine numbers: $-36 + 36 = 0$.
* Final expression: $15b$

Final Answer:
1.) $5c + 20$
2.) $10y - 30$
3.) $8a + 20b$
4.) $6c + 6a + 9b$
5.) $17x + 30$
6.) $10x + 17$
7.) $25 + 25t$
8.) $10q + 5m$
9.) $5m + 32$
10.) $15b$