What number should be added to the expression x2+2x to change it into a perfect square trinomial?
Answer: To make the expression x2 + 2x a perfect square, we need to add 1 to it.
Let's look into the steps below.
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.