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2.1 Adding and Multiplying Polynomials Secondary Math II Notes OBJECTIVE: Correctly simplify polynomials expressions using addition, subtraction, and multiplication. Use the distributive property to multiply binomials, trinomials, and polynomials. Simplifying Expressions- Addition and Subtraction Identify and combine any like terms in the expression below. 3x 2 + 14x 3x 2 + 4 y 1 + 2y 2 4 y 21 y 2 + 4x 2 12 z + 7x 3x + 14 x + 7 x = 24 x 2 + 1 = 3 3x 2 + 4 x 2 = 1x 2 4 y + 4 y = 0 2 y 2 + 21y 2 = 19 y 2 12 z + 12 z A. 2 9 + 2x + 3x 2 5x + 10 1 3x 2 3x + 2 B. 2 x 3 + 2 x 2 + 4 x + 8 ( ) + 6 x 3 + 5 x 2 2 x 7 ( ) 8 x 3 + 7 x 2 + 2 x + 1 C. x 2 + 3x 7 ( ) 3x 3 + 2 x 2 4 ( ) 3x 3 x 2 + 3x 3 D. 5 x 2 3x + 4 ( ) 4 x 2 3x 11 ( ) x 2 + 15 Addition Multiplication 3 + x = 3 + x 3 x = 3x x + x = 2 x x x = x 2 x + x + x = 3x x x x = x 3 x + x = 0 x x = x 2 2 x + 3x = 5 x 2 x 3x = 6 x 2 7 x + x = 8 x 7 x x = 7 x 2 4 x + 5 y = 4 x + 5 y 4 x 5 y = 20 xy 2 x + x 2 = 2 x + x 2 2 x x 2 = 2 x 3 x + x 2 + x 3 = x + x 2 + x 3 x x 2 x 3 = x 6 3x 2 + 5 y 4 = 3x 2 + 5 y 4 3x 2 5 y 4 = 15 x 2 y 4 3x 2 + 5 y 4

2 2.1 TN Adding and Multiplying Polynomials · Adding and Multiplying Polynomials 2.1 Secondary Math II Notes OBJECTIVE: Correctly simplify polynomials expressions using addition,

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Page 1: 2 2.1 TN Adding and Multiplying Polynomials · Adding and Multiplying Polynomials 2.1 Secondary Math II Notes OBJECTIVE: Correctly simplify polynomials expressions using addition,

    2.1 Adding and Multiplying Polynomials

Secondary Math II Notes

OBJECTIVE: Correctly simplify polynomials expressions using addition, subtraction, and multiplication. Use the distributive property to multiply binomials, trinomials, and polynomials.

Simplifying Expressions- Addition and Subtraction  Identify  and  combine  any  like  terms  in  the  expression  below.

3x −2+14x −3x 2 +4y −1+2y 2 −4y −21y 2 +4x 2 −12z +7x  3x +14x + 7x = 24x−2+−1= −3−3x2 + 4x2 =1x2

4y+−4y = 02y2 +−21y2 = −19y2

−12z+−12z

A.    

 2−9+2x +3x 2 −5x +10−1  3x2 −3x + 2        

B.  

2x3 + 2x2 + 4x +8( )+ 6x3 + 5x2 − 2x − 7( )    

8x3 + 7x2 + 2x +1  C.    

 

x2 +3x − 7( )− 3x3 + 2x2 − 4( )  −3x3 − x2 +3x −3  

D.    

5x2 −3x + 4( )− 4x2 −3x −11( )  

x2 +15  Addition   Multiplication

3+ x = 3+ x   3⋅ x = 3x  x + x = 2x   x ⋅ x = x2  x + x + x = 3x   x ⋅ x ⋅ x = x3  −x + x = 0   −x ⋅ x = −x2  2x +3x = 5x   2x ⋅3x = 6x2  7x + x = 8x   7x ⋅ x = 7x2  4x + 5y = 4x + 5y   4x ⋅5y = 20xy  2x + x2 = 2x + x2   2x ⋅ x2 = 2x3  x + x2 + x3 = x + x2 + x3   x ⋅ x2 ⋅ x3 = x6  3x2 + 5y4 = 3x2 + 5y4   3x2 ⋅5y4 =15x2y4 3x2 + 5y4  

Page 2: 2 2.1 TN Adding and Multiplying Polynomials · Adding and Multiplying Polynomials 2.1 Secondary Math II Notes OBJECTIVE: Correctly simplify polynomials expressions using addition,

 

Multiplying by a Monomial  

2 x + 9( )  

2x +18

−5 x2 + 4x − 2( )  

−5x2 − 20x +10

3x −x −11( )  

−3x2 −33x

−2x2 x2 − 5x +3( )  

−2x4 +10x3 − 6x2

Multiplying by a Binomial  

x + 2( ) x −3( )  

x2 −3x + 2x − 6x2 − x − 6

3x +3( ) 2x + 7( )  

6x2 + 21x + 6x + 216x2 + 27x + 21

x2 + 4x( ) x3 + 4x2 +1( )  

x5 + 4x4 + x2 + 4x4 +16x3 + 4xx5 +8x4 +16x3 + x2 + 4x

3x +1( ) 3x −1( )  

9x2 +3x −3x −19x2 −1

2x + 5( ) 2x + 5( )  

4x2 +10x +10x + 254x2 + 20x + 25

x3 + x2( ) x2 + x( )  

x5 + x4 + x4 + x3

x5 + 2x4 + x3

Multiplying by a Trinomial  

x2 + 2x +3( ) x2 + 5x − 6( )  

x4 + 5x3 − 6x2 + 2x3 +10x2 −12x +3x2 +15x −18x4 + 7x3 + 7x2 +3x −18

x2 +3x − 2( ) y2 + 5y+1( )  

x2y2 + 5x2y+ x2 +3xy2 +15xy+3x − 2y2 −10y− 2