Exercise 44 Page 61

Practice makes perfect

We want to write an expression that represents the area of the shaded region.

To do so, we need to find the difference between the areas of the squares. Area of Big Square: & (4n+1)^2 Area of Small Square: & 5^2 Let's find the difference.

(4n+1)^2-5^2

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

16n^2+8n+1-5^2

CalcPow

Calculate power

16n^2+8n+1-25

SubTerm

Subtract term

16n^2+8n-24

This expression represents the area of the shaded region.

Our goal is to find the dimensions of a rectangle with the same area as the shaded region. To find the dimensions, we need to factor the expression 16n^2+8n-24 in such a way that it is a product of two binomials. Thus, each binomial represents one of the dimensions.

16n^2+8n-24

WriteDiff

Write as a difference

16n^2-16n+24n-24

▼

Factor out 16n & 24

FactorOut

Factor out 16n

16n(n-1)+24n-24

FactorOut

Factor out 24

16n(n-1)+24(n-1)