Transcript Add and Subtract Polynomials

Do Now
Simplify.
 12a bc

3 4 7
 48a b c
3
2



2
Polynomials
A polynomial is a sum of monomials.
Common polynomials:
A binomial is a sum of two monomials.
A trinomial is a sum of three monomials.
Standard Form
The terms of a polynomial are usually written so
that the powers of the variable are in
descending form.
(the powers go from greatest to least)
Ex. Write 7x2 – 11 + 2x4 in standard form.
2x4 + 7x2 – 11
Rewrite each polynomial so that the powers of x
are in descending form.
1) 6x2 + 5 – 8x – 2x3
2) 2xy3 + y2 + 5x3 – 3x2y
Adding & Subtracting Polynomials
To add or subtract polynomials,
1) Align The Like Terms
2) Add/Subtract The Like Terms
*Subtracting is the same as adding the opposite!!
** When adding or subtracting,
EXPONENTS STAY THE SAME!!
1. Add the following polynomials (9y
– 7x + 15a) + (-3y + 8x – 8a)
Line up your like terms.
9y – 7x + 15a
+ -3y + 8x – 8a
_________________________
6y + x + 7a
2. Add the following polynomials
(3a2 + 3ab – b2) + (4ab + 6b2)
+
3a2 + 3ab – b2
4ab + 6b2
_________________________
3a2 + 7ab + 5b2
3. Add the following polynomials
(4x2 – 2xy + 3y2) + (-3x2 – xy + 2y2)
Line up your like terms.
4x2 – 2xy + 3y2
+ -3x2 – xy + 2y2
_________________________
x2 - 3xy + 5y2
4. Subtract the following polynomials
(9y – 7x + 15a) – (-3y +8x – 8a)
Line up your like terms and add the
opposite.
9y – 7x + 15a
+
(+
3y
–
8x
+
8a)
-------------------------------------12y – 15x + 23a
5. Subtract the following polynomials
(7a – 10b) – (3a + 4b)
7a – 10b
+ (– 3a – 4b)
--------------------------------------
4a – 14b
6. Subtract the following polynomials
(4x2 – 2xy + 3y2) – (-3x2 – xy + 2y2)
4x2 – 2xy + 3y2
+ (+ 3x2 + xy – 2y2)
--------------------------------------
7x2 – xy + y2
From Comes First!!!!
7. Subtract (2x2 – 5a2 + 7x) from
(5x2 + 3a2 – 5x).
(5x2 + 3a2 – 5x) – (2x2 – 5a2 + 7x)
The polynomial after FROM goes first!!!!
5x2 + 3a2 – 5x
+ (- 2x2 + 5a2 – 7x)
-------------------------------------3x2 + 8a2 – 12x
2
(5x
8. Subtract
– 4) from
(3x2 + 8x + 4).
(3x2 + 8x + 4) – (5x2 – 4)
3x2 + 8x + 4
+ (- 5x2
+ 4)
--------------------------------------2x2 + 8x + 8
Find the sum or difference.
(5a – 3b) + (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 3b
Find the sum or difference.
(5a – 3b) – (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 9b
Homework
Chapter 8 Packet:
pg. 474 #’s 10 – 20 evens
pg. 481 multiples of 3
* Lab Packets Due Next Lab