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STUDY GUIDE NOTES - CHAPTER 9
Monomial – is a single term. Each of the items below is a monomial.
3x4
5x
-7
8y
x8
6xy
-17m
3b
-4p9
-ab
A binomial consists of 2 monomials that do not have like terms.
Like terms means the monomials can be combined. The variable part of the monomials are exactly the same.
9x2 and -7 x2 are like terms they both include x2 !
Combine the monomials where they can be combined. Cross out the boxes where the monomials do not have
like terms and cannot be combined. (HINT: Only 3 boxes contain like terms.)
3x4 + 4x4 =
5x + 6 =
-7 + 2x4 =
8y – 4y =
x8 + 8x =
6xy + 7 =
-17m + 6m =
5b3 - 3b =
-4p3 + 9 =
-ab + 7b =
A trinomial has 3 monomial terms that do not have like terms.
3x2 – 6x + 8
Adding polynomials - add the like terms! DO NOT CHANGE ANY EXPONENT!
(5x2 + 6) + (3x2 + x + 4) = 8x2 + x + 10
Subtracting polynomials – Change to an addition problem by changing the sign in front of the parenthesis and
of all the terms in the second parenthesis—then add the like terms!
DO NOT CHANGE ANY EXPONENT!
(3x2 + 6x + 5) – (5x2 – 7x + 11)
(3x2 + 6x + 5) + (-5x2 + 7x - 11) = 3x2 -5x2 + 6x + 7x + 5 – 11 = -2x2 + 13x - 6
Multiplying a monomial by a polynomial.
Multiply each term by multiplying the coefficients (the number in front of the variable) and adding the
exponents of the variables.
2x ( 3x6 – 4x3 + 2x2 + 5) = 6x7 – 8x4 + 4x3 + 10x
Multiplying two binomials ---use FOIL - FIRST, OUTER, INNER, LAST
Then combine like terms.
(2x – 6)(4x +5) = 8x2 +10x -24x – 30 = 8x2 – 14x – 30
Multiplying a trinomial by a binomial-- Multiply each term of the binomial by each term of the trinomial and
then combine all like terms.
(3x +5)(6x2 + 2x – 8) = 3x(6x2 + 2x – 8) + 5(6x2 + 2x – 8)
= 18x3 + 6x2 – 24x + 30x2 +10x – 40
= 18x3 + 36x2 – 14x – 40
Special cases – use FOIL to solve
Rewrite (x + 7)2 = (x + 7)(x + 7) = x2 + 7x + 7x + 49 = x2 + 14x + 49
When both terms in a binomial are the same and one is adding and one is subtracting—After FOIL the middle
terms will cancel each other out. Just solve using FOIL.
(3x + 7) (3x – 7) = 9x2 -21x +21x – 49 = 9x2 – 49
Finding the shaded region.
x+3
(2x + 1) (x + 3) = 2x2 + 6x + x + 3 = 2x2 + 7x + 3
x+2
3x
STEP 1: Find the area of the big rectangle.
STEP 2: Find the area of the small rectangle.
3x(x + 2) = 3x2 + 6x
2x + 1
STEP 3: Find the big rectangle MINUS the small rectangle.
(2x2 + 7x + 3) – (3x2 + 6x)
(2x2 + 7x + 3) + (–3x2 – 6x)
-x2 + x +3
the area of the shaded region