Respuesta :
The expression as a perfect square trinomial is [tex]\rm x^2+4x+4\\[/tex].
The expression as a perfect square trinomial is [tex]\rm x^2-20x+100\\[/tex]
The expression as a perfect square trinomial is [tex]\rm x^2+4x+\dfrac{25}{4}\\[/tex].
Given that
The given equations are as follows;
[tex]\rm x^2 + 2x + \\\\ x^2 -20x +\\\\ x^2 + 5x +\\\\[/tex]
We have to determine
What values are needed to make each expression a perfect square trinomial?
According to the question
To know more about the values are needed to make a perfect square trinomial following all the steps given below.
A perfect square trinomial is equal to;
[tex]\rm (x+a)^2 = x^2+a^2+2ax[/tex]
1. The given equation is,
[tex]\rm x^2 + 2x +[/tex]
Then,
Compare with the formula of a perfect square trinomial.
[tex]\rm x^2+2ax+a^2= x^2+4x\\ \\ 4x=2ax\\ \\ a = \dfrac{4x}{2x}\\ \\ a=2[/tex]
Substitute the value of a
[tex]\rm x^2+2ax+a^2= x^2+4x+(2)^2\\ \\ x^2+2ax+a^2= x^2+4x+4\\[/tex]
The expression as a perfect square trinomial is [tex]\rm x^2+4x+4\\[/tex].
2. The given equation is,
[tex]\rm x^2 - 20x +[/tex]
Then,
Compare with the formula of a perfect square trinomial.
[tex]\rm x^2+2ax+a^2= x^2-20x\\ \\ -20x=2ax\\ \\ a = \dfrac{-20x}{2x}\\ \\ a=-10[/tex]
Substitute the value of a
[tex]\rm x^2+2ax+a^2= x^2 -20x+(-10)^2\\ \\ x^2+2ax+a^2= x^2-20x+100\\[/tex]
The expression as a perfect square trinomial is [tex]\rm x^2-20x+100\\[/tex].
3. The given equation is,
[tex]\rm x^2 + 5x +[/tex]
Then,
Compare with the formula of a perfect square trinomial.
[tex]\rm x^2+2ax+a^2= x^2+5x\\ \\ 5x=2ax\\ \\ a = \dfrac{5x}{2x}\\ \\ a=\dfrac{5}{2}[/tex]
Substitute the value of a
[tex]\rm x^2+2ax+a^2= x^2+4x+(\dfrac{5}{2})^2\\ \\ x^2+2ax+a^2= x^2+4x+\dfrac{25}{4}\\[/tex]
The expression as a perfect square trinomial is [tex]\rm x^2+4x+\dfrac{25}{4}\\[/tex].
To know more about Trinomial Click the link given below.
https://brainly.com/question/1224704
