polynomial expressions unit 2, lesson 2 a1.1.1.5.1
TRANSCRIPT
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Polynomial Expressions
Unit 2, Lesson 2
A1.1.1.5.1
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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!!!!
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Example A(π₯3β2π₯+8 )+(7 π₯2+2 π₯β5 )
ππ+πππ+π
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Example B(7 π₯2+2 π₯β5 )+(π₯3β2π₯2+4 π₯+8 )
ππ+πππ+π π+π
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Example C(2 π¦2+6 π¦β2 )β ( π¦2β2 π¦+7 )
ππ+π π βπ
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Example D(2 π₯3β5π₯2+3 π₯β9 )+ (π₯3+6 π₯2+11 )
π ππ+ππ+π π+π
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Example E(5 π₯3β π₯2+10 π₯ )β (6 π₯3+5 π₯2β7 π₯ )
βππβπ ππ+πππ
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Example F(4 π₯3β2π₯2+5 )β (βπ₯3β π₯2+4 π₯β2 )
π ππβππβπ π+π
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Example G
, , and
π ππβπ ππ+π+π π+ππ
Add the polynomials
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Example H
π ππβπ π+ππππ βπ ππ
Subtract from
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Example I
βππβπ π+πππ+π ππ
Subtract from
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Example J
, , and
βππ+π ππ π+π π ππ+π ππ
Add the polynomials
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Example K
, , and
π ππ π+π π ππ+π πβπβππ+π ππ
Add the polynomials
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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.
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1 Term 2 Terms Example A
7 π₯ (2 π₯β1 )
ππππβππ
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1 Term 2 Terms Example B
β3 π₯ (4 π₯+8 )
βππππβπππ
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1 Term 2 Terms Example C
5 π₯π¦ (2π₯+3 π¦β4 )
πππππ+πππ ππβππ ππ
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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.
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2 Terms 2 Termsβ’ There is a nifty pneumonic to help you remember the
procedure.
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2 Terms 2 Terms Example D
(3 π₯+2 ) (4 π₯β5 )
ππππβπ πβππ
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2 Terms 2 Terms Example E
(2 π₯+1 ) (3 π₯+7 )
π ππ+πππ+π
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2 Terms 2 Terms Example F
(8 π₯β2 ) (2π₯β3 )
ππππβπππ+π
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2 Terms 2 Terms Example G
(9 π₯π¦β4 ) (5 π₯+7 )
πππππ+ππ ππβπππβππ
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Terms Termsβ’ Multiply each and every term in
the first polynomial by each and every term of the second polynomial.
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Terms Terms Example H
(π₯β4 ) (3 π₯β π¦+3 )
π ππβπ π+π π βππβππ
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Terms Terms Example IWhat is the product of
and ?
βπ ππβππ πβππ ππ+πππ+ππππ
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Terms Terms Example JWhat is the product of
and ?
πππβππβππππ+πππ+πππβπ
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Terms Terms Example KWhat is the product of
, and ?
ππππ=π ππβπππ+ππ
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Example #1
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Example #2
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Example #3
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Example #4
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Example #5
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Example #6
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Example #7
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Example #8
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Example #9