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Multiply and simplify each expression below:

 Apr 22, 2019
 #1
avatar+100483 
+2

a)  ( x + 1) ( 2x^2  - 3)    =   x * 2x^2   + 1 * 2x^2  - 3*x   - 3 * 1  =  2x^3 + 2x^2 - 3x - 3

 

cool cool cool

 Apr 22, 2019
 #2
avatar+100483 
+2

b)   (x + 1)  (x^2 - 2x + 3)

 

We can do this just lke regular multiplication

 

x^2   -  2x  + 3

              x + 1

_______________

x^2   -   2x   +  3

x^3  -  2x^2  + 3x

________________________

x^3 + x^2 - 2x^2 - 2x + 3x + 3      combine like terms

 

x^3  - x^2   + x  + 3

 

 

cool  cool cool

 Apr 22, 2019
 #3
avatar+100483 
+2

c)   2 ( x + 3)^3  =  2 ( x + 3) (x + 3) ( x + 3)  =

 

2 [ x^2 + 6x + 9 ]  (x + 3)  =

 

[ x^2  + 6x + 9 ]  (2) ( x + 3)  =

 

(x^2 + 6x + 9) ( 2x + 6)  =

 

x^2  +  6x   +  9

           2x  +   6

_________________

6x^2 + 36x + 54

2x^3 +12x^2 + 18x 

 

6x^2 + 2x^3  + 12x^2 + 36x + 18x + 54  =

 

2x^3 + 18x^2 + 54x + 54

 

cool cool cool

 Apr 22, 2019
 #4
avatar+100483 
+2

d)  ( x + 1) (2x - 3)^2  =   (x + 1) (2x - 3) (2x - 3)   =  (x + 1) ( 4x^2 - 12x + 9)

 

4x^2  -  12x  + 9

                x  +  1

_____________

4x^2  -   12x  + 9

4x^3 - 12x^2 + 9x

____________________________

4x^2 + 4x^3 - 12x - 12x^2 + 9 + 9x           combine like terms

 

4x^3  + 4x^2 - 12x^2 - 12x + 9x + 9

 

4x^3 -  8x^2  - 3x  + 9

 

 

cool cool cool

 Apr 22, 2019

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