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Polynomial Expressions
Unit 2, Lesson 2
A1.1.1.5.1
Adding and Subtracting Polynomials
• To add and subtract polynomials, simply combine like terms.
o Combine the coefficients.
o DO NOT change the variables and their exponents!!!!
Example A(𝑥3−2𝑥+8 )+(7 𝑥2+2 𝑥−5 )
𝒙𝟑+𝟕𝒙𝟐+𝟑
Example B(7 𝑥2+2 𝑥−5 )+(𝑥3−2𝑥2+4 𝑥+8 )
𝒙𝟑+𝟓𝒙𝟐+𝟔 𝒙+𝟑
Example C(2 𝑦2+6 𝑦−2 )− ( 𝑦2−2 𝑦+7 )
𝒚𝟐+𝟖 𝒚 −𝟗
Example D(2 𝑥3−5𝑥2+3 𝑥−9 )+ (𝑥3+6 𝑥2+11 )
𝟑 𝒙𝟑+𝒙𝟐+𝟑 𝒙+𝟐
Example E(5 𝑥3− 𝑥2+10 𝑥 )− (6 𝑥3+5 𝑥2−7 𝑥 )
−𝒙𝟑−𝟔 𝒙𝟐+𝟏𝟕𝒙
Example F(4 𝑥3−2𝑥2+5 )− (−𝑥3− 𝑥2+4 𝑥−2 )
𝟓 𝒙𝟑−𝒙𝟐−𝟒 𝒙+𝟕
Example G
, , and
𝟐 𝒙𝟑−𝟐 𝒙𝟐+𝒙+𝟓 𝒚+𝒙𝒚
Add the polynomials
Example H
𝟓 𝒙𝟐−𝟗 𝒚+𝟏𝟏𝒙𝒚 −𝟓 𝒚𝟐
Subtract from
Example I
−𝒙𝟐−𝟕 𝒙+𝟏𝟏𝒚+𝟓 𝒚𝟐
Subtract from
Example J
, , and
−𝒙𝟑+𝟔 𝒙𝟐 𝒚+𝟓 𝒙 𝒚𝟐+𝟑 𝒚𝟑
Add the polynomials
Example K
, , and
𝟕 𝒙𝟐 𝒚+𝟑 𝒙 𝒚𝟐+𝟓 𝒙−𝟖−𝟑𝒚+𝟒 𝒙𝒚
Add the polynomials
Multiplying Polynomials
• To multiply polynomials, multiply each and every term in the first polynomial by each and every term of the second polynomial.
• Combine like terms.
1 Term 2 Terms Example A
7 𝑥 (2 𝑥−1 )
𝟏𝟒𝒙𝟐−𝟕𝒙
1 Term 2 Terms Example B
−3 𝑥 (4 𝑥+8 )
−𝟏𝟐𝒙𝟐−𝟐𝟒𝒙
1 Term 2 Terms Example C
5 𝑥𝑦 (2𝑥+3 𝑦−4 )
𝟏𝟎𝒙𝟐𝒚+𝟏𝟓𝒙 𝒚𝟐−𝟐𝟎 𝒙𝒚
2 Terms 2 Terms• The process for multiplying
binomials remains the same. You multiply each term of the first binomial with each term of the second binomial.
• There is a nifty pneumonic to help you remember the procedure.
2 Terms 2 Terms• There is a nifty pneumonic to help you remember the
procedure.
2 Terms 2 Terms Example D
(3 𝑥+2 ) (4 𝑥−5 )
𝟏𝟐𝒙𝟐−𝟕 𝒙−𝟏𝟎
2 Terms 2 Terms Example E
(2 𝑥+1 ) (3 𝑥+7 )
𝟔 𝒙𝟐+𝟏𝟕𝒙+𝟕
2 Terms 2 Terms Example F
(8 𝑥−2 ) (2𝑥−3 )
𝟏𝟔𝒙𝟐−𝟐𝟖𝒙+𝟔
2 Terms 2 Terms Example G
(9 𝑥𝑦−4 ) (5 𝑥+7 )
𝟒𝟓𝒙𝟐𝒚+𝟔𝟑 𝒙𝒚−𝟐𝟎𝒙−𝟐𝟖
Terms Terms• Multiply each and every term in
the first polynomial by each and every term of the second polynomial.
Terms Terms Example H
(𝑥−4 ) (3 𝑥− 𝑦+3 )
𝟑 𝒙𝟐−𝟗 𝒙+𝟒 𝒚 −𝒙𝒚−𝟏𝟐
Terms Terms Example IWhat is the product of
and ?
−𝟔 𝒙𝟐−𝟏𝟖 𝒙−𝟐𝟎 𝒚𝟐+𝟐𝟒𝒚+𝟐𝟑𝒙𝒚
Terms Terms Example JWhat is the product of
and ?
𝟔𝒂𝟐−𝟕𝒂−𝟐𝟎𝒃𝟐+𝟏𝟕𝒃+𝟕𝒂𝒃−𝟑
Terms Terms Example KWhat is the product of
, and ?
𝟏𝟐𝒙𝟑=𝟖 𝒙𝟐−𝟐𝟕𝒙+𝟏𝟖
Example #1
Example #2
Example #3
Example #4
Example #5
Example #6
Example #7
Example #8
Example #9