polynomial expressions unit 2, lesson 2 a1.1.1.5.1
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Polynomial Expressions
Unit 2, Lesson 2
A1.1.1.5.1
Adding and Subtracting Polynomials
β’ To add and subtract polynomials, simply combine like terms.
o Combine the coefficients.
o DO NOT change the variables and their exponents!!!!
Example A(π₯3β2π₯+8 )+(7 π₯2+2 π₯β5 )
ππ+πππ+π
Example B(7 π₯2+2 π₯β5 )+(π₯3β2π₯2+4 π₯+8 )
ππ+πππ+π π+π
Example C(2 π¦2+6 π¦β2 )β ( π¦2β2 π¦+7 )
ππ+π π βπ
Example D(2 π₯3β5π₯2+3 π₯β9 )+ (π₯3+6 π₯2+11 )
π ππ+ππ+π π+π
Example E(5 π₯3β π₯2+10 π₯ )β (6 π₯3+5 π₯2β7 π₯ )
βππβπ ππ+πππ
Example F(4 π₯3β2π₯2+5 )β (βπ₯3β π₯2+4 π₯β2 )
π ππβππβπ π+π
Example G
, , and
π ππβπ ππ+π+π π+ππ
Add the polynomials
Example H
π ππβπ π+ππππ βπ ππ
Subtract from
Example I
βππβπ π+πππ+π ππ
Subtract from
Example J
, , and
βππ+π ππ π+π π ππ+π ππ
Add the polynomials
Example K
, , and
π ππ π+π π ππ+π πβπβππ+π ππ
Add the polynomials
Multiplying Polynomials
β’ To multiply polynomials, multiply each and every term in the first polynomial by each and every term of the second polynomial.
β’ Combine like terms.
1 Term 2 Terms Example A
7 π₯ (2 π₯β1 )
ππππβππ
1 Term 2 Terms Example B
β3 π₯ (4 π₯+8 )
βππππβπππ
1 Term 2 Terms Example C
5 π₯π¦ (2π₯+3 π¦β4 )
πππππ+πππ ππβππ ππ
2 Terms 2 Termsβ’ The process for multiplying
binomials remains the same. You multiply each term of the first binomial with each term of the second binomial.
β’ There is a nifty pneumonic to help you remember the procedure.
2 Terms 2 Termsβ’ There is a nifty pneumonic to help you remember the
procedure.
2 Terms 2 Terms Example D
(3 π₯+2 ) (4 π₯β5 )
ππππβπ πβππ
2 Terms 2 Terms Example E
(2 π₯+1 ) (3 π₯+7 )
π ππ+πππ+π
2 Terms 2 Terms Example F
(8 π₯β2 ) (2π₯β3 )
ππππβπππ+π
2 Terms 2 Terms Example G
(9 π₯π¦β4 ) (5 π₯+7 )
πππππ+ππ ππβπππβππ
Terms Termsβ’ Multiply each and every term in
the first polynomial by each and every term of the second polynomial.
Terms Terms Example H
(π₯β4 ) (3 π₯β π¦+3 )
π ππβπ π+π π βππβππ
Terms Terms Example IWhat is the product of
and ?
βπ ππβππ πβππ ππ+πππ+ππππ
Terms Terms Example JWhat is the product of
and ?
πππβππβππππ+πππ+πππβπ
Terms Terms Example KWhat is the product of
, and ?
ππππ=π ππβπππ+ππ
Example #1
Example #2
Example #3
Example #4
Example #5
Example #6
Example #7
Example #8
Example #9