Question

Make the expression a perfect square u^2 + 10u + 

Answer 1

Take the coefficient of "u"

10

divide it by 2

5

square it

25

So, a perfect square would be

u^2 + 10u +25

which would be

(u +5)^2

Explanation:

Answer 2

To form a perfect square trinomial from the expression u^2 + 10u + n, the value of n must be 25, resulting in the perfect square (u + 5)^2.

To make the expression u^2 + 10u + n a perfect square, you need to determine the value of n that turns the expression into a perfect square trinomial. A perfect square trinomial is of the form (a+b)^2 = a^2 + 2ab + b^2.

Here, we compare the given expression with the standard form. We identify that a = u and 2ab = 10u. This tells us that 2ab/2a = b, so 10u/2u = 5. Hence, b = 5. Therefore, the last term b^2 should be 5^2 = 25 for the expression to be a perfect square.

So, if we want to make u^2 + 10u + n a perfect square, the value of n must be 25, making the expression (u + 5)^2.a