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^2-24x+____

( )^2

Answer 1

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).

Answer 2

Answer:

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

Step-by-step explanation:

We are given an expression $x^2-24x+\_\_$

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

Using identity $(a-b)^2=a^2+b^2-2ab$

Comparing the above identity with the given expression,

We get $a^2=x^2 \rightarrow a=x$ and $-2ab=-24x$

$-2ab=-24x \Rightarrow ab=12x$

Thus, b = 12

and $b^{2}=144$

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