Warm Up

1
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
2
Warm Up Write the opposite of each integer. 1.
10 Subtract. 3. 19 (12) Add. 5. (3x2 7)
(x2 3x) 6. (2m2 3m) (5m2 2)
10
2. 7
7
31
4. 16 21
37
4x2 3x 7
3m2 3m 2
Pre-Algebra
3
Problem of the Day Tara has 4 pairs of shorts, 3
tops, and 2 pairs of sandals. If she wants to
wear a completely different outfit than she wore
yesterday, how many combinations does she have to
choose from?
6
Pre-Algebra
4
Learn to subtract polynomials.
Pre-Algebra
5
Subtraction is the opposite of addition. To
subtract a polynomial, you need to find
its opposite.
Pre-Algebra
6
Additional Example 1A 1B Finding the Opposite
of a Polynomial
Find the opposite of each polynomial.
A. 8x3y4z2
(8x3y4z2)
The opposite of a is a.
8x3y4z2
B. 3x4 8x2
(3x4 8x2)
Distribute the sign.
3x4 8x2
Pre-Algebra
7
Additional Example 1C Finding the Opposite of a
Polynomial
Find the opposite of the polynomial.
A. 9a6b4 a4b2 1
(9a6b4 a4b2 1)
Distribute the sign.
9a6b4 a4b2 1
Pre-Algebra
8
Insert Lesson Title Here
Try This Example 1A 1B
Find the opposite of each polynomial.
A. 4d2e3f3
(4d2e3f3)
4d2e3f3
The opposite of a is a.
B. 4a2 4a4
(4a2 4a4)
Distribute the sign.
4a2 4a4
Pre-Algebra
9
Insert Lesson Title Here
Try This Example 1C
Find the opposite of the polynomial.
A. 9a6b4 a4b2 1
(9a6b4 a4b2 1)
9a6b4 a4b2 1
Distribute the sign.
Pre-Algebra
10
To subtract a polynomial, add its opposite.
Pre-Algebra
11
Additional Example 2A Subtracting Polynomials
Horizontally
Subtract.
A. (5x2 2x 3) (3x2 8x 4)
Add the opposite.
(5x2 2x 3) (3x2 8x 4)
Associative property.
5x2 2x 3 3x2 8x 4
2x2 6x 1
Combine like terms.
Pre-Algebra
12
Additional Example 2B Subtracting Polynomials
Horizontally
Subtract.
B. (b2 4b 1) (7b2 b 1)
Add the opposite.
(b2 4b 1) (7b2 b 1)
Associative property.
b2 4b 1 7b2 b 1
6b2 5b
Combine like terms.
Pre-Algebra
13
Insert Lesson Title Here
Try This Example 2A
Subtract.
A. (2y3 3y 5) (4y3 3y 5)
Add the opposite.
(2y3 3y 5) (4y3 3y 5)
Associative property.
2y3 3y 5 4y3 3y 5
2y3
Combine like terms.
Pre-Algebra
14
Insert Lesson Title Here
Try This Example 2B
Subtract.
B. (c3 2c2 3) (4c3 c2 1)
(c3 2c2 3) (4c3 c2 1)
Add the opposite.
c3 2c2 3 4c3 c2 1
Associative property.
3c3 3c2 4
Combine like terms.
Pre-Algebra
15
You can also subtract polynomials in a vertical
format. Write the second polynomial below the
first one, lining up the decimal points.
Pre-Algebra
16
Additional Example 3A Subtracting Polynomials
Vertically
Subtract.
A. (2n2 4n 9) (6n2 7n 5)
(2n2 4n 9)
2n2 4n 9
(6n2 7n 5)
6n2 7n 5
Add the opposite.
4n2 3n 4
Pre-Algebra
17
Additional Example 3B Subtracting Polynomials
Vertically
Subtract.
B. (10x2 2x 7) (x2 5x 1)
(10x2 2x 7)
10x2 2x 7
(x2 5x 1)
x2 5x 1
Add the opposite.
9x2 3x 8
Pre-Algebra
18
Additional Example 3C Subtracting Polynomials
Vertically
Subtract.
C. (6a4 3a2 8) (2a4 7)
(6a4 3a2 8)
6a4 3a2 8
(2a4 7)
2a4 7
Add the opposite.
8a4 3a2 15
Pre-Algebra
19
Insert Lesson Title Here
Try This Example 3A
Subtract.
A. (4r3 4r 6) (6r3 3r 3)
(4r3 4r 6)
4r3 4r 6
Add the opposite.
(6r3 3r 3)
6r3 3r 3
2r3 r 3
Pre-Algebra
20
Insert Lesson Title Here
Try This Example 3B
Subtract.
B. (13y2 2x 5) (y2 5x 9)
(13y2 2x 5)
13y2 2x 5
(y2 5x 9)
y2 5x 9
Add the opposite.
12x2 7x 14
Pre-Algebra
21
Insert Lesson Title Here
Try This Example 3C
Subtract.
C. (5x2 2x 5) (3x2 7x)
(5x2 2x 5)
5x2 2x 5
3x2 7x
(3x2 7x)
Add the opposite.
8x2 9x 5
Pre-Algebra
22
Additional Example 4 Business Application
Suppose the cost in dollars of producing x
bookcases is given by the polynomial 250
128x, and the revenue generated from sales is
given by the polynomial 216x 75. Find a
polynomial expression for the profit from
producing and selling x bookcases, and evaluate
the expression for x 95.
216x 75 (250 128x)
revenue cost
Add the opposite.
216x 75 (250 128x)
Associative Property
216x 75 250 128x
Combine like terms.
88x 325
Pre-Algebra
23
Additional Example 4 Continued
The profit is given by the polynomial 88x 325.
For x 95,
88(95) 325 8360 325 8035
The profit is 8035.
Pre-Algebra
24
Insert Lesson Title Here
Try This Example 4
Suppose the cost in dollars of producing x
baseball bats is given by the polynomial
6 12x, and the revenue generated from sales is
given by the polynomial 35x 5. Find a
polynomial expression for the profit from
producing and selling x baseball bats, and
evaluate the expression for x 50.
35x 5 (6 12x)
revenue cost
Add the opposite.
35x 5 (6 12x)
Associative Property
35x 5 6 12x
23x 11
Combine like terms.
Pre-Algebra
25
Insert Lesson Title Here
Try This Example 4 Continued
The profit is given by the polynomial 23x 11.
For x 50,
23(50) 11 1150 11 1139
The profit is 1139.
Pre-Algebra
26
Insert Lesson Title Here
Lesson Quiz
Find the opposite of each polynomial.
Subtract. 3. (3z2 7z 6) (2z2 z
12)
2. 3m3 2m2n
3m3 2m2n
1. 3a2b2c3
3a2b2c3
z2 8z 18
4. 18h3 (4h3 h2 12h 2) 5. (3b2c 5bc2
8b2) (4b2c 2bc2 c2)
22h3 h2 12h 2
b2c 3bc2 8b2 c2
Pre-Algebra