Exercise 18 Page P6

Practice makes perfect

a Let's introduce variables so we can use algebra to work out the answers.

Description	Variable
Side length of the current square shaped office.	a
Width of the new rectangular office.	w
Length of the new rectangular office.	l

We are given information on how the dimensions of the office will be changing. Let's express this information in terms of the variables.

Description	Expression
The new office is 3 feet wider than the old office.	w=a+3
The new office is 5 feet longer than the old office.	l=a+5

b The area of a rectangle is the product of its length and width. Let's use the expressions from Part A to find this product. We can use the Distributive Property to find the polynomial expression, which is the product of the two binomials.

A=l w

SubstituteII

l= a+5, w= a+3

A=( a+5)( a+3)

▼

Simplify right-hand side

Distr

Distribute (a+3)

A=a(a+3)+5(a+3)

Distr

Distribute a

A=a^2+3a+5(a+3)

Distr

Distribute 5

A=a^2+3a+5a+15

AddTerms

Add terms

A=a^2+8a+15

The area of Monica's new office in terms of the side length of her current square-shaped office is a^2+8a+15 square feet.

c We can substitute a=7 into the expression we got in Part B to find the area of Monica's new office.

A=a^2+8a+15

Substitute

a= 7

A= 7^2+8( 7)+15

▼

Simplify right-hand side

CalcPowProd

Calculate power and product

A=49+56+15

AddTerms

Add terms

A=120

The area of Monica's new office is 120 square feet. To find the difference compared to the current office space, we need to subtract. Note that her current office is a square, so it's area is 7^2=49 square feet. Expansion:120-49=71square feet

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Exercise 18 Page P6

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