Question

Fill in the blank with a number to make the expression a perfect square.

U^2 + 2u + ?

Answer 1

u² + 2u + 1

Explanation:

In the question it's asking to find the the number in the blank to make the expression a perfect square.

Let the number in the blank be 'x'.

To guess 'x' , use the algebraic identity :-
`(a + b)^2 = a^2 + (2 * a * b) + b^2`

While matching the expression with identity , the expression will look like this :- u² + 2ux + x²

In the expression given in the question , it's "2u" but after matching the expression with identity , it is found to be "2ux".

⇒ x = 1 (∵ If x will be 1 , then 2ux = 2×u×1 = 2u)

⇒ x² = 1

∴ The number in the blank is 1.