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I have no idea what to do here:

 

If ab = 10 and a^2 + b^2 = 40, then find (a + b)^4 - (a - b)^4.

 Dec 24, 2020
 #1
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ab   =10

a^2  + b^2  = 40

 

( a + b)^4 =  a^4  + 4a^3b  + 6a^2b^2  + 4ab^3  + b^4     (1)

(a  - b)^4  =  a^4  - 4a^3b  +  6a^2b^2  -  4ab^3  + b^4    (2)

 

Subtract  (2)  from (1)  and we get that

 

8a^3b + 8ab^3  =    8(ab)( a^2  + b^2)

 

Now....just fill in what we  know

 

8 (ab) (a ^2 + b^2)   =

 

8 (10) (40)  =  

 

3200

 

 

cool cool cool

 Dec 24, 2020

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