Question

factor each expression.

1. 45c + 10d
2. 27 - 9x + 15y

solve. show each step.

1. a construction worker bought several bottles of juice for $3 at the convenience store. she paid for them with a $20 bill. if j represents the number of bottles of juice, write an expression for the change she should receive.
2. a giant bamboo plant grew an average of 18 centimeters per year. the botanist started measuring the plant when it was 5 centimeters tall. if y represents the number of years the botanist has measured the plant, what expression represents its height?

Explanation:

Problem 7: Factor \( 45c + 10d \)

Step 1: Find GCF of 45 and 10

Factors of 45: \( 1, 3, 5, 9, 15, 45 \)
Factors of 10: \( 1, 2, 5, 10 \)
GCF is \( 5 \).

Step 2: Factor out GCF

\( 45c + 10d = 5(9c + 2d) \)

Step 1: Find GCF of 27, 9, 15

Factors of 27: \( 1, 3, 9, 27 \)
Factors of 9: \( 1, 3, 9 \)
Factors of 15: \( 1, 3, 5, 15 \)
GCF is \( 3 \).

Step 2: Factor out GCF

\( 27 - 9x + 15y = 3(9 - 3x + 5y) \)

Step 1: Cost of \( j \) bottles

Cost = \( 3j \) dollars.

Step 2: Change = Total paid - Cost

Change = \( 20 - 3j \)

Answer:

\( 5(9c + 2d) \)

Problem 8: Factor \( 27 - 9x + 15y \)