Question

Find the number that must be added to each expression to form a perfect square trinomial. Then write the trinomial as a binomial squared.

x^2+6x+____

( )^2

Answer 1

(3)²

x²+6x+9 = (x+3)²

Explanation:

Given expression is

x²+6x + _____

We have to complete above trinomial so that it makes perfect square.

We use following formula.

a²+2ab+b² = (a+b)²

as comparing given expression with above formula,we get

a² = x² ⇒ a = x

2ab = 6x ⇒2ab = 2(x)(3)

Hence , the value of b is 3.

putting the value of b in formula , we conclude that

(x)²+2(x)(3)+(3)² = (x+3)²

x²+6x+9 = (x+3)²

Hence, the given trinomial x²+6x+9 is square of binomial (x+3).

Answer 2

i.
`(3)^2` or
`9`

ii.
`(x+3)^2`

Explanation:

The given expression is

`x^2+6x+----`

We add half the coefficient of x squared, which is

`((6)/(2) )^2`

This simplifies to;

`(3)^2`

Or

`9`

Based on the question, you must write 3 inside
`(\:)^2`

We add
`(3)^2` to obtain
`x^2+6x+(3)^2`

The expression as a binomial squared is

`=(x+3)^2`