Replace * with a monomial so that the derived expression may be represented as a square of a binomial

Question

b^2+20b+∗

b²+20b+∗

Answer 1

Hi Kiranpreet.

 

I think they are attempting to get you to do a process we call "Completing the Square".

 

If you take the coefficient of the "x" term and divide it by 2, you get 20/2 = 10

 

Now square this and get 10²= 100.

 

If you add this squared term to b²+20b  you will have

 

b²+ 20b + 100    and this is

 

(b+10)²

 

So want to ADD 100

 

This makes it the SQUARE of (b+10), a binomial.

 

Hope that  helps.   :-)