1. EXAMPLE 1 a. –5(–7) = 35 b. –8(2) = –16 c. –12(0) = 0
Multiplying Integers
a. –5(–7)
= 35
The product of two integers with the same sign is positive.
b. –8(2)
= –16
The product of two integers with different signs is negative.
c. –12(0)
= 0
The product of an integer and 0 is 0.

2. b. Evaluate xyz when x = 2, y = –4, and z = 6.
EXAMPLE 2
Evaluating Variable Expressions
a. Evaluate a2 when a = –3.
b. Evaluate xyz when x = 2, y = –4, and z = 6.
SOLUTION
a. a2
= (–3)2
Substitute –3 for a.
= –3(–3)
Write –3 as a factor two times.
= 9
Multiply –3 and –3.
b. xyz
= 2(–4)(6)
Substitute 2 for x, –4 for y, and 6 for z.
= –8(6)
Multiply 2 and –4.
= –48
Multiply –8 and 6.

3. EXAMPLE 3
Using Integer Multiplication
Greenland
Most of Greenland is covered with ice that is almost two miles thick in some places. Scientists estimate that 3 feet of this ice melts each year. Find the change in the thickness of the ice after 10 years.

4. Change in ice thickness = –3(10) = –30
EXAMPLE 3
Using Integer Multiplication
SOLUTION
You can find the total change in the ice thickness by multiplying the yearly change by the number of years. Use – 3 for the yearly change because the thickness of the ice decreases by 3 feet each year.
Change in ice thickness = –3(10)
= –30
ANSWER
The thickness of the ice will decrease 30 feet in 10 years.

5. GUIDED PRACTICE Find the product. 1. –9(2) 3. 5(–5) ANSWER –18 ANSWER
for Examples 1, 2, and 3
Find the product.
1. –9(2)
(–5)
ANSWER
–18
ANSWER
–25
2. –3(–4)
(–14)
ANSWER 12
ANSWER

6. 5. Evaluate the expressions x2y and –3xy2 when x = –2 and y = 3.
GUIDED PRACTICE
for Examples 1, 2, and 3
5. Evaluate the expressions x2y and –3xy2 when x = –2
and y = 3.
ANSWER
12, 54
What If?
What is the change in the thickness of the ice in Example 3 after 18 years? 6.
ANSWER
– 54 ft