Exercise 45 Page 212

Practice makes perfect

a Any expression in the form

a (b)

is equivalent to multiplying

a

and

b .

5 x (3 x) = 5 x \cdot 3 x \Leftrightarrow 5 \cdot x \cdot 3 \cdot x

Note that multiplication is commutative, so we can rearrange the factors any way we want without changing the result.

5 \cdot x \cdot 3 \cdot x

Commutative Property of Multiplication

5 \cdot 3 \cdot x \cdot x

15 x \cdot x

$a \cdot a = a^{2}$

15 x^{2}

b When adding two

x -

terms, we can factor out

x

and add the coefficients.

5 x + 3 x

Factor out $x$

(5 + 3) x

Add terms

8 x

c Any expression in the form

a (b)

is equivalent to multiplying

a

and

b .

6 x \cdot x

$a \cdot a = a^{2}$

6 x^{2}

d When adding two variables, we can factor out

x

and then add the coefficients.

6 x + x

Factor out $x$

(6 + 1) x

Add terms

7 x

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

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