1. Homework Solution: lesson 7.3 page 446
37) x(x+3)(x-1) 38) x(x-6)(x+5) 39) x(x-3)(x+1) 43) (𝑥 2 +4)(𝑥−3) 44) (𝑥 2 −1)(𝑥+3) 45) (𝑥 2 −5)(𝑥−2)

2. Homework
Lesson 7.1_page 430 #39-46 ALL

3. Lesson 7.1 Adding and Subtracting Polynomials

4. Objectives The student will be able to:
1. add and subtract polynomials.
SOL: A.2b
Designed by Skip Tyler, Varina High School

5. Like Terms
Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers.
Which terms are like? a2b, 4ab2, 3ab, -5ab2
4ab2 and -5ab2 are like.
Even though the others have the same variables, the exponents are not the same.
3a2b = 3aab, which is different from 4ab2 = 4abb.

6. Constants are like terms.
Which terms are like? x, -3, 5b, 0
-3 and 0 are like.
Which terms are like? x, 2x2, 4, x
3x and x are like.
Which terms are like? wx, w, 3x, 4xw
2wx and 4xw are like.

7. 1. Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)
Combine your like terms.
3a2 + 3ab + 4ab - b2 + 6b2
3a2 + 7ab + 5b2

8. 2. Add the following polynomials using column form: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
Line up your like terms.
4x2 - 2xy + 3y2
+ -3x2 - xy + 2y2
_________________________
x2 - 3xy + 5y2

9. Adding Polynomials
Some people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms!
(x2 + 3x + 1)
+ (4x )
(x2 + 3x + 1) + (4x2 +5)
5x2 + 3x + 6
add these polynomials: (2a2+3ab+4b2) + (7a2+ab+-2b2)
(2a2 + 3ab + 4b2)
+ (7a2 + ab + -2b2)
(2a2+3ab+4b2) + (7a2+ab+-2b2)
9a2 + 4ab + 2b2

10. Adding Polynomials
Add the following polynomials; you may stack them if you prefer:

11. Subtracting Polynomials
Subtract: (3x2 + 2x + 7) - (x2 + x + 4)
Step 1: Change subtraction to addition (Keep-Change-Change.).
(3x2 + 2x + 7) + (- x2 - x - 4)
Step 2: Underline OR line up the like terms and add.
(3x2 + 2x + 7)
+ (- x2 + - x + - 4)
2x x + 3

12. Rewrite subtraction as adding the opposite.
3. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)
Rewrite subtraction as adding the opposite.
(9y - 7x + 15a) + (+ 3y - 8x + 8a)
Group the like terms.
9y + 3y - 7x - 8x + 15a + 8a
12y - 15x + 23a

13. 4. Subtract the following polynomials: (7a - 10b) - (3a + 4b)
Rewrite subtraction as adding the opposite.
(7a - 10b) + (- 3a - 4b)
Group the like terms.
7a - 3a - 10b - 4b
4a - 14b

14. Subtracting Polynomials
Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add:

15. Write each sum or difference as a polynomial in standard form
Write each sum or difference as a polynomial in standard form. Then classify the polynomial by degree and by number of terms.
(𝑥 4 + 5𝑥 2 +𝑥)−( 2𝑥 3 +𝑥+𝑥 4 −4)

16. Simplify by finding the perimeter:
9.1 Adding and Subtracting Polynomials
Simplify by finding the perimeter:
x2 + x
c2 + 1
6c + 3 A B
2x2
2x2
4c2 + 2c + 5
x2 + x
A = 5c2 + 8c + 9
B = 6x2 + 2x

17. Simplify by finding the perimeter:
9.1 Adding and Subtracting Polynomials
Simplify by finding the perimeter:
2d2 + d – 4
3x2 – 5 x D C
3d2 – 5d
x2 + 7
3d2 – 5d
d2 + 7
D = 9d2 – 9d + 3
C = 8x2 – 10x + 14

18. Simplify by finding the perimeter:
9.1 Adding and Subtracting Polynomials
Simplify by finding the perimeter:
3x2 – 5x
a3 + 2a
a + 1 E F
x2 + 3
2a3 + a + 3
E = 3a3 + 4a + 4
F = 8x2 – 10x + 6