Exercise 22 Page 202

a Let's look at what the Distributive Property states for any three terms

a,

b,

and

c .

a (b + c) = a b + a c

Let's use it in this example!

5 x (x - 6)

Distr

Distribute $5 x$

5 x \cdot x - 5 x \cdot 6

Multiply

5 x^{2} - 30 x

The product simplifies to

5 x^{2} - 30 x .

b Since we have used the Distributive Property in Part A, we can draw and label a generic rectangle for this case. We have

2

factors in this product:

- 9 y

and

(6 - 3 y) .

Let's draw a generic rectangle and label each side accordingly.

Inside each part of the rectangle we write the product of its height and length. In the rectangle above we can see what product we should evaluate. Let's do it!

We know that the area of this rectangle is

- 9 y (6 - 3 y) .

We can also state it as a sum using the areas of the

2

parts of the rectangle, which we determined above.

- 9 y (6 - 3 y) = - 45 y + 27 y^{2}

Subchapter links

4.1.1 Line of Best Fit p.196-197

4.1.2 Residuals p.201-202

4.1.3 Upper and Lower Bounds p.205-206

4.1.4 Least Squares Regression Line p.210-213