Question

simplify each expression.

1. (100 + 4z)20
2. 0.75(3.5a - 6b)

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.

1. 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 5: Simplify \((100 + 4z)20\)

Step 1: Apply the distributive property

We use the distributive property \(a(b + c)=ab+ac\), here \(a = 20\), \(b=100\) and \(c = 4z\). So we have \(20\times100+20\times4z\)

Step 2: Calculate the products

\(20\times100 = 2000\) and \(20\times4z=80z\)

Step 1: Apply the distributive property

Using the distributive property \(a(b - c)=ab - ac\), where \(a = 0.75\), \(b = 3.5a\) and \(c=6b\). So we get \(0.75\times3.5a-0.75\times6b\)

Step 2: Calculate the products

\(0.75\times3.5a=2.625a\) and \(0.75\times6b = 4.5b\)

Step 1: Find the GCF of 45 and 10

The factors of \(45\) are \(1,3,5,9,15,45\) and the factors of \(10\) are \(1,2,5,10\). The greatest common factor (GCF) of \(45\) and \(10\) is \(5\)

Step 2: Factor out the GCF

We factor out \(5\) from each term. \(45c=5\times9c\) and \(10d = 5\times2d\). So \(45c + 10d=5(9c + 2d)\)

Answer:

\(2000 + 80z\)

Problem 6: Simplify \(0.75(3.5a-6b)\)