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.

Answer 1

(x+3)² is the perfect square of the given expression.

Explanation:

We have given the expression :

x² +6x+ ?

We have to complete the square.

x² +6x

x² +2(x)(3)

Adding (3)² we get,

x² +2(x)(3) +(3)²

Now it becomes square .

(x+3)² is the perfect square of the given expression.

Answer 2

Add:

`{3}^(2)`

The perfect square binomial is:

`( {x + 3)}^(2)`

EXPLANATION

The give expression is;

`{x}^(2) + 6x`

Add half the square of the coefficient of x.

Thus,

`( { (6)/(2) })^(2) = {3}^(2)`

We add to get,

`{x}^(2) + 6x + 9`

The perfect square binomial is,

`( {x + 3)}^(2)`