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

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

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

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

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`