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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

Respuesta :

kudzordzifrancis

Answer:

i. [tex](3)^2[/tex] or [tex]9[/tex]

ii. [tex](x+3)^2[/tex]

Step-by-step explanation:


The given expression is


[tex]x^2+6x+----[/tex]


We add half the coefficient of x squared, which is

[tex](\frac{6}{2} )^2[/tex]


This simplifies to;

[tex](3)^2[/tex]

Or

[tex]9[/tex]


Based on the question, you must write 3 inside [tex](\:)^2[/tex]


We add   [tex](3)^2[/tex] to obtain [tex]x^2+6x+(3)^2[/tex]

The expression as a binomial squared is

[tex]=(x+3)^2[/tex]

zainebamir540

Answer:

(3)²

x²+6x+9 =  (x+3)²

Step-by-step 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).


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