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Expand the product (x - 2)^2 (x + 2)^2 (x - 3). What is the product of the nonzero coefficients of the resulting expression, including the constant ter

 Feb 10, 2022
 #1
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In steps

 

Note that (x + 2)^2  (x - 2)^2   can be written as

 

[  (x + 2) ( x - 2) ] ^2   =   ( x^2 - 4]^2  =  x^4 - 8x^2 + 16

 

So

 

(x - 3)   (x^4 - 8x^2   + 16 )  =

 

(x^5 -8x^3 + 16x) + ( -3x^4 + 24x^2 - 48)  =

 

1x^5 - 3x^4  - 8x^3  + 24x^2 + 16x  - 48

 

Now  we just need to multiply

 

(1) (-3) (-8) (24) (16) (-48)   =  -442368

 Feb 10, 2022

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