Fill in the blank to make the expression a perfect square. u^2-2u+ ____

Question

jamesj · Answer

If this is a perfect square, it is of the form
$$ (u+a)^2 = u^2 + 2ua + a^2 $$
Hence what is the value of a?

anonymous · Answer

I have to find the value of a, but it's not making sense

jamesj · Answer

Your expression is 
$$ u^2 - 2u + \_\_\_ $$ and it must be equal to $$ u^2 + 2au + a^2 $$.

Compare the coefficients of u.  This gives you an equation for a.

jamesj · Answer

i.e., it must be the coefficients of u are equal.  The coefficient of u in your expression is -2.  That must be equal to what?

jamesj · Answer

The coefficient of u in the second equation is 2a.  Hence if the two polynomials are equal, it must be that
-2 = 2a.

Therefore a = ...what?

anonymous · Answer

-1

anonymous · Answer

thank you!