Question

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

Answer 1

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?

Answer 2

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

Answer 3

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.

Answer 4

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?

Answer 5

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?

Answer 6

-1

Answer 7

thank you!