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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^2-24x+____

( )^2

Respuesta :

Answer:

Thus, when 144 is added to the given expression [tex]x^2-24x+144[/tex] to form a perfect square trinomial of [tex](x-12)^2[/tex]

Step-by-step explanation:

We are given an expression [tex]x^2-24x+\_\_[/tex]

We have find the number such that expression form a perfect square trinomial.

Using identity [tex](a-b)^2=a^2+b^2-2ab[/tex]

Comparing the above identity with the given expression,

We get [tex]a^2=x^2 \rightarrow a=x[/tex] and [tex]-2ab=-24x[/tex]

[tex]-2ab=-24x \Rightarrow ab=12x[/tex]

Thus, b = 12

and [tex]b^{2}=144[/tex]

Thus, when 144 is added to the given expression [tex]x^2-24x+144[/tex] to form a perfect square trinomial of [tex](x-12)^2[/tex]





zainebamir540

Answer:

-12 is number that is when added to given expression to form perfect square.


Step-by-step explanation:

Given expression is :

x²-24x + _____

We have to make above expression complete square.

We use following formula to complete this question.

a²+2ab+b² = (a+b)²

Comparing given expression to above formula ,we get

a² = x² ⇒ a = x

2ab = -24x

2ab = 2(x)(-12)

hence, the value of b is -12.

Putting the value of b in above formula,we get

(x)²+2(x)(-12)+(-12)² = x²-24x+144

(x-12)² = x²-24x+144

Hence, the trinomial x²-24x+144 is square of binomial (x-12).



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