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.\(Assuming\:that\:x\:\ne \:-5,\:simplify\:\frac{\left(2x\:+\:10\right)^4}{\left(x\:+\:5\right)^3}. \)

 Jul 16, 2023
 #1
avatar+570 
0

 

Simplify    

                           (2x + 10)4      

                          ––––––––      

                             (x + 5)3          

 

Factor the (x + 5)'s out of the numerator   

so you can cancel out the denominator.  

 

I'll write it out real simple.  Actually, I have to,   

if I'm going to keep those exponents straight.  

 

                           (2)(x + 5) • (2)(x + 5) • (2)(x + 5) • (2)(x + 5)   

                          –––––––––––––––––––––––––––––––—–––     

                                (x + 5)   •   (x + 5)   •   (x + 5)             

 

 

                          Which leaves      8 (x + 5)    

.

 Jul 16, 2023
 #2
avatar+570 
0

 

CORRECTION to my above.   

An error has been pointed out to me. 

 

The answer should be 16 (x+ 5)    

 

Of course it should.  

Bosco  Jul 17, 2023

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