Exercise 64 Page 169

a Let's build a generic rectangle where the factor

(x + 2)

represents the horizontal side and the factor

(x - 5)

represents the vertical side.

By multiplying the vertical and horizontal sides of the smaller rectangles that are inside the generic rectangle, we can calculate their areas.

Finally we will calculate the products.

The product of the expressions is the sum of the smaller rectangles area.

x^{2} + 2 x - 5 x - 10 ⇕ x^{2} - 3 x - 10

b Like in Part A, we will create a generic rectangle with each factor representing each side.

Like in Part A, we multiply the smaller rectangle's sides.

Finally we will calculate the products.

Again, we will add the areas of the smaller rectangles.

y^{2} + 3 x y + 2 x y + 6 x^{2} ⇕ y^{2} + 5 x y + 6 x^{2}

c As we did in previous Parts, we can create a generic rectangle where the factors represents each side of the generic rectangle.

Like in Part A and B, we multiply the smaller rectangles side.

Let's calculate each of the products.

Let's add the areas of the smaller rectangles.

- 3 x y + 8 x + 3 y^{2} - 8 y

d As we did in previous Parts, we will create a generic rectangle where the factors represents its two sides.

Let's multiply the side of the smaller rectangles.

Finally we will calculate the products.

Now we add the areas of the smaller rectangles to find the product of the original expression.

x^{2} + 3 x y - 3 x y - 9 y^{2} ⇕ x^{2} - 9 y^{2}

4.2.1 Solving Systems of Equations Using Substitution p.156-157

4.2.2 Making Connections: Systems, Solutions, and Graphs p.162-163

4.2.3 Solving Systems Using Elimination p.168-169

4.2.4 More Elimination p.173

4.2.5 Choosing a Strategy for Solving Systems p.176-177