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# What number should be added to the expression x^{2}+2x to change it into a perfect square trinomial?

**Solution:**

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

Given expression: x^{2 }+ 2x

Let the constant value to be added be c^{2}, to make the expression a perfect square.

Thus, the expression becomes: x^{2 }+ 2x + c^{2}

We know the algebraic identity (x + c)^{2 }= x^{2} + c^{2} + 2xc

Comparing x^{2} + c^{2} + 2xc with our expression x^{2 }+ 2x + c^{2},

x^{2} + c^{2} + 2xc = x^{2 }+ 2x + c^{2}

Thus, we get

2xc = 2x

Hence, c = 1

Therefore, c^{2} = 1

Thus, x^{2 }+ 2x + c^{2} = x^{2 }+ 2x + 1 = (x + 1)^{2}

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

## What number should be added to the expression x^{2}+2x to change it into a perfect square trinomial?

**Summary:**

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

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