Download 2. - JYMath

EXAMPLE 1
Apply the distributive property
Use the distributive property to write an equivalent expressi
a.
4(y + 3) = 4y + 12
b.
(y + 7)y = y2 + 7y
c.
n(n – 9) = n2 – 9n
d.
(2 – n)8 =16 – 8n
EXAMPLE 2 Distribute a negative number
Use the distributive property to write an equivalent
expression.
a.
–2(x + 7)= – 2(x) + – 2(7)
= – 2x – 14
b. (5 – y)(–3y) = 5(–3y) – y(–3y)
= – 15y + 3y2
Distribute – 2.
Simplify.
Distribute – 3y.
Simplify.
EXAMPLE 2 Distribute a negative number
c.
–(2x – 11) = (–1)(2x – 11)
= (– 1)(2x) – (–1)(11)
Multiplicative property
of 21
Distribute – 1.
= – 2x + 11
Simplify.
EXAMPLE 3
Identify parts of an expression
Identify the terms, like terms, coefficients, and
constant terms of the expression 3x – 4 – 6x + 2.
SOLUTION
Write the expression as a sum: 3x + (–4) + (–6x) + 2
Terms: 3x, – 4, – 6x, 2
Like terms: 3x and – 6x; – 4 and 2
Coefficients: 3, – 6
Constant terms: – 4, 2
GUIDED PRACTICE
for Examples 1, 2 and 3
Use the distributive property to write an equivalent expression.
1.
2(x + 3) = 2x + 6
2.
– (4 – y) = – 4 + y
3.
(m – 5)(– 3m) = m (– 3m) –5 (– 3m)
= – 3m2 + 15m
1
4. (2n + 6) 1 = 2n 1 + 6
2
2
2
=n+3
Distributive – 1
Distributive – 3m
Simplify.
Distribute
1
2
Simplify.
GUIDED PRACTICE
for Examples 1, 2 and 3
Identify the terms, like terms, coefficients, and
constant terms of the expression – 7y + 8 – 6y – 13.
SOLUTION
Write the expression as a sum: – 7y + 8 – 6y – 13
Terms: – 7y, 8, – 6y, – 13
Like terms: – 7y and – 6y , 8 and – 13;
Coefficients: – 7, – 6
Constant terms: 8, – 13
EXAMPLE 4
Standardized Test Practice
Simplify the expression 4(n + 9) – 3(2 + n).
A 5n + 30
B n + 30
C 5n + 3
4(n + 9) – 3(2 + n) = 4n + 36 – 6 – 3n
= n + 30
D n+3
Distributive property
Combine like terms.
ANSWER
The correct answer is B. A
B
C
D
EXAMPLE 5
Solve a multi-step problem
EXERCISING
Your daily workout plan involves a
total of 50 minutes of running and
swimming. You burn 15 calories per
minute when running and 9 calories
per minute when swimming. Let r be
the number of minutes that you run.
Find the number of calories you burn
in your 50 minute workout if you run
for 20 minutes.
SOLUTION
The workout lasts 50 minutes, and your running time is
r minutes. So, your swimming time is (50 – r) minutes.
EXAMPLE 5
Solve a multi-step problem
STEP 1
Write a verbal model. Then write an equation.
Amount
burned
(calories)
=
Burning rate
when running
(calories/minute)
•
C
=
5
C = 15r + 9(50 – r)
Running
time
(minutes)
r
+
+
Burning rate
when swimming
(calories/minute)
•
9
r) Write equation.
= 15r + 450 – 9r
Distributive property
= 6r + 450
Combine like terms.
Swimming
time
(minutes)
(50 –
EXAMPLE 5
Solve a multi-step problem
STEP 2
Find the value of C when r = 20.
Write equation.
C = 6r + 450
= 6(20) + 450 = 570
Substitute 20 for r. Then simplify.
ANSWER
You burn 570 calories in your 50 minute workout if you
run for 20 minutes.
GUIDED PRACTICE
6.
for Examples 4 and 5
Simplify the expression 5(6 + n) – 2(n – 2).
SOLUTION
5(6 + n) – 2(n – 2) = 30 + 5n – 2n + 4
= 34 + 3n
Distributive property
Combine like terms.
GUIDED PRACTICE
7.
for Examples 4 and 5
WHAT IF? In Example 45, suppose your workout
lasts 45 minutes. How many calories do you run
for 20 minutes? 30 minutes?
SOLUTION
The workout lasts 45 minutes, and your running time is
r minutes. So, your swimming time is (45 – r) minutes.
for Examples 4 and 5
GUIDED PRACTICE
STEP 1
Write a verbal model. Then write an equation.
Amount
burned
(calories)
C
=
Burning rate
when running
(calories/minute)
=
•
Running
time
(minutes)
15
C = 15 r + 9 (45 – r)
r
+
Burning rate
when swimming
(calories/minute)
+
•
9
Write equation.
= 15r + 405 – 9r
Distributive property
= 6r + 405
Combine like terms.
Swimming
time
(minutes)
(45 – r)
GUIDED PRACTICE
for Examples 4 and 5
STEP 2
Find the value of C when r = 20.
C = 6r + 405
= 6(20) + 405 = 525
Write equation.
Substitute 20 for r. Then simplify.
STEP 3
Find the value of C when r = 30.
C = 6r + 405
= 6(30) + 405 = 585
Write equation.
Substitute 30 for r. Then simplify.
GUIDED PRACTICE
for Examples 4 and 5
ANSWER
You burn 525 calories in your 45 minute workout if you
run for 20 minutes.
You burn 585 calories in your 45 minute workout if you
run for 30 minutes.