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# What number should be added to the expression x^{2 }+ 4x to change it into a perfect square trinomial?

**Solution:**

A perfect square trinomial is defined as an algebraic expression that is obtained by

squaring a binomial expression.

Given, the expression is x^{2} + 4x + C -------- (1)

A perfect square is an expression in the form (x+a)² which can be written in a trinomial form as

(x + a)^{2} = (x + a)(x + a) = x^{2} + ax + ax + a^{2}

(x+a)^{2} = x^{2} + 2ax + a^{2} -------------------------- (2)

Comparing (1) and (2)

2a = 4

a = 2

Also, a^{2} = C

C = (2)^{2} = 4

Therefore, the number that should be added is 4.

**Aliter:**

A function that can be obtained by squaring the binomial expression is a perfect square trinomial. It satisfies the condition b^{2 }- 4ac = 0 and are in the form of ax^{2} + bx + c.

As per the question, b = coefficient of x, a = coefficient of x^{2} and c = constant term.

⇒ b^{2 }- 4ac = 0

⇒ b^{2 }= 4ac

⇒ (4)^{2 }= 4 (1) c

⇒ 16^{ }= 4 × c

By dividing both the sides by 4, we get

⇒ c = 4

## What number should be added to the expression x^{2 }+ 4x to change it into a perfect square trinomial?

**Summary:**

The number that should be added to the expression x^{2}+4x to change it into a perfect square trinomial is 4.

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