What number should be added to the expression x²+2x to change it into a perfect square trinomial?

Solution:

Perfect squares are numbers that are obtained by squaring a whole number. 

Given expression: x² + 2x

Let the constant value to be added be c², to make the expression a perfect square.

Thus, the expression becomes:  x² + 2x + c²

We know the algebraic identity (x + c)² = x² + c² + 2xc 

Comparing x² + c² + 2xc  with our expression x² + 2x + c²,

x² + c² + 2xc = x² + 2x + c²

Thus, we get

 2xc = 2x

Hence, c = 1

Therefore, c² = 1

Thus, x² + 2x + c² = x² + 2x + 1 = (x + 1)²

Therefore, to make the expression x² + 2x a perfect square, we need to add 1 to it. 

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What number should be added to the expression x²+2x to change it into a perfect square trinomial?

Summary:

To make the expression x² + 2x a perfect square, we need to add 1 to it.