1. Adding and Subtracting Polynomials
Really just means “Combine Like Terms”
Adding:
Combine the terms with Same Variable and Same Exponent.
DO NOT change the variable or exponent… just add coefficients
(5x3 + 7x2 – 6x + 8) (2x3 – x2 – 2)
Subtracting:
The subtraction gets distributed through the entire 2nd polynomial
CHANGE ALL THE SIGNS
Then add like above
(9x2 – 7x + 2) (4x2 – 2x – 8)
(9x2 – 7x + 2) x2 + 2x + 8

2. Multiply by a Monomial
Distribute the monomial to EVERY term of the polynomial.
Multiply the coefficients
Add the exponents
Watch out for signs
Examples:
4t (t + 6)
4t2 + 24t
(c+8) 2c
2c2 + 16c
6y(y2 + 7y + 2)
6y3 + 42y2 + 12y
-3g2 (-9g3 + 4g)
27g5 – 12g3
You Try:
10x (-4x2 + x – 3)
CHALLENGE: find the shaded area
6x3 ( 3x2 – x + 10)
3x2 + 5x - 1
8z2 (4z3 + 2z2 – 5z)
2x2 + 4x 7x 3x

3. Multiply binomials Method #1:
List each binomial along top and side of a box
In each section, multiply the monomials together
Check for “like terms” to add
List answers in standard form x +2
Exp 1: (x + 2) (x+1)
x2 +3x +2 x x2 2x +1 x 2 b -4
Exp 5: (5b+9)(b-4)
5b2
-20b 5b
5b2 -11b -36 9 9b
-36 7y
-3x 9
14xy
-6x2 2x
Exp 9:(2x+5y)(7y-3x) 5y
35y2
-15xy
-6x2 – 1xy + 35y2

4. Multiplying Binomials (Part 2)
F.O.I.L. (A shortcut)
This is an option for multiplying binomials WITHOUT drawing a box.
The letters remind us which terms to multiply so that we include all of them.
First
Outside
Inside
Last
Still Multiply each set of terms together then ADD all the parts. Look for LIKE terms to combine in the middle.
(3x + 6) (2x + 5)
FIRST: (3x)(2x) = 6x2
OUTSIDE: (3x)(5) = 15x
(3x + 6) (2x + 5)
(3x + 6) (2x + 5)
INSIDE: (6)(2x) = 12x
6x2 + 27x + 30
(3x + 6) (2x + 5)
LAST: (6)(5) = 30
EX: (4x+5)(3x-7)
12x2
-28x
+15x
-35
12x2 -13x - 35
EX: (6x+1)(4x-9)
24x2
-54x
+4x -9
24x2 -50x - 9