Creative Publications Algebra With Pizzazz Answer Key Flash Sales ... - Free Printable

Problem Analysis

The task involves using the distributive property to simplify or factor expressions. The distributive property states:
\[
a(b + c) = ab + ac
\]
This property allows us to either distribute a factor across a sum or factor out a common term from a sum.

The worksheet provides several expressions and asks us to identify the correct application of the distributive property. We will solve each part step by step.

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Step-by-Step Solution

#### 1. Identify the Distributive Property in Each Expression
We need to match each expression with its simplified or factored form using the distributive property.

#### 2. Solve Each Expression

##### Expression 1: \( 7(x + 8) = 7x + \_\_\_ \)
- Distribute \( 7 \) across \( (x + 8) \):
\[
7(x + 8) = 7x + 7 \cdot 8 = 7x + 56
\]
- Answer: \( 56 \)

##### Expression 2: \( 45 + x = 20 + \_\_\_ \)
- This expression does not directly involve the distributive property. It seems to be a simple algebraic manipulation.
- Rearrange to isolate terms:
\[
45 + x = 20 + (x + 25)
\]
- Answer: \( x + 25 \)

##### Expression 3: \( 2(3x + 9) = \_\_\_ \)
- Distribute \( 2 \) across \( (3x + 9) \):
\[
2(3x + 9) = 2 \cdot 3x + 2 \cdot 9 = 6x + 18
\]
- Answer: \( 6x + 18 \)

##### Expression 4: \( 0.3x + 1.1x = \_\_\_ \)
- Combine like terms:
\[
0.3x + 1.1x = (0.3 + 1.1)x = 1.4x
\]
- Answer: \( 1.4x \)

##### Expression 5: \( 8y + 10y = \_\_\_ \)
- Combine like terms:
\[
8y + 10y = (8 + 10)y = 18y
\]
- Answer: \( 18y \)

##### Expression 6: \( 2(7x + 4y) = \_\_\_ \)
- Distribute \( 2 \) across \( (7x + 4y) \):
\[
2(7x + 4y) = 2 \cdot 7x + 2 \cdot 4y = 14x + 8y
\]
- Answer: \( 14x + 8y \)

##### Expression 7: \( 6(9 + 5m) = \_\_\_ \)
- Distribute \( 6 \) across \( (9 + 5m) \):
\[
6(9 + 5m) = 6 \cdot 9 + 6 \cdot 5m = 54 + 30m
\]
- Answer: \( 54 + 30m \)

##### Expression 8: \( 3(8x + 2y) = \_\_\_ \)
- Distribute \( 3 \) across \( (8x + 2y) \):
\[
3(8x + 2y) = 3 \cdot 8x + 3 \cdot 2y = 24x + 6y
\]
- Answer: \( 24x + 6y \)

##### Expression 9: \( 2(4x + 10) = 2x + \_\_\_ \)
- Distribute \( 2 \) across \( (4x + 10) \):
\[
2(4x + 10) = 2 \cdot 4x + 2 \cdot 10 = 8x + 20
\]
- Answer: \( 20 \)

##### Expression 10: \( 3(12 + 3y) = \_\_\_ \)
- Distribute \( 3 \) across \( (12 + 3y) \):
\[
3(12 + 3y) = 3 \cdot 12 + 3 \cdot 3y = 36 + 9y
\]
- Answer: \( 36 + 9y \)

##### Expression 11: \( x = \_\_\_ \)
- This expression is incomplete and does not provide enough information to solve. It might be a placeholder or an error.

##### Expression 12: \( y = \_\_\_ \)
- Similar to Expression 11, this is incomplete and cannot be solved.

##### Expression 13: \( 2y = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 14: \( 3a = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 15: \( k = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 16: \( 4 = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 17: \( u = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 18: \( a = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 19: \( b + v = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 20: \( m = \_\_\_ \)
- This expression is incomplete and cannot be solved.

##### Expression 21: \( 2(y + 15) = \_\_\_ \)
- Distribute \( 2 \) across \( (y + 15) \):
\[
2(y + 15) = 2 \cdot y + 2 \cdot 15 = 2y + 30
\]
- Answer: \( 2y + 30 \)

##### Expression 22: \( a(b + n) = \_\_\_ \)
- Distribute \( a \) across \( (b + n) \):
\[
a(b + n) = ab + an
\]
- Answer: \( ab + an \)

##### Expression 23: \( \frac{2}{5}(b + n) = \_\_\_ \)
- Distribute \( \frac{2}{5} \) across \( (b + n) \):
\[
\frac{2}{5}(b + n) = \frac{2}{5} \cdot b + \frac{2}{5} \cdot n = \frac{2b}{5} + \frac{2n}{5}
\]
- Answer: \( \frac{2b}{5} + \frac{2n}{5} \)

##### Expression 24: \( \frac{3}{4}c = \_\_\_ (a + b + c) \)
- This expression is incomplete and cannot be solved without additional context.

##### Expression 25: \( ay = a(7x + \_\_\_) \)
- Factor out \( a \) from \( ay \):
\[
ay = a(7x + y)
\]
- Answer: \( y \)

##### Expression 26: \( ky = \_\_\_ (4x + 11y) \)
- Factor out \( k \) from \( ky \):
\[
ky = k(4x + 11y)
\]
- Answer: \( k \)

##### Expression 27: \( by = y(\_\_\_ + 8b) \)
- Factor out \( y \) from \( by \):
\[
by = y(b + 8b)
\]
- Answer: \( b \)

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Final Answers

\[
\boxed{
\begin{array}{l}
56, x + 25, 6x + 18, 1.4x, 18y, 14x + 8y, 54 + 30m, 24x + 6y, 20, 36 + 9y, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, \text{(incomplete)}, 2y + 30, ab + an, \frac{2b}{5} + \frac{2n}{5}, \text{(incomplete)}, y, k, b
\end{array}
}
\]