Respuesta :
Answer:
Option A :[tex]y^{2} +20y+100[/tex]
Option D: [tex]y^{2} +18y+81[/tex]
Step-by-step explanation:
To Find: Which trinomials are perfect square trinomials?
option A :[tex]y^{2} +20y+100[/tex]
Factorizing:
[tex]y^{2} +10y+10y+100[/tex]
[tex]y(y+10)+10(y+10)[/tex]
[tex](y+10)(y+10)[/tex]
[tex](y+10)^{2}[/tex]
Hence Option A is perfect square
Option B : [tex]y^{2} +25y+200[/tex]
Since this cannot be factorized
Hence not a perfect square
Option C: [tex]y^{2} +6y+36[/tex]
Since this cannot be factorized
Hence not a perfect square
Option D: [tex]y^{2} +18y+81[/tex]
[tex]y^{2} +9y+9y+81[/tex]
[tex]y(y+9)+9(y+9)[/tex]
[tex](y+9)(y+9)[/tex]
[tex](y+9)^{2}[/tex]
Hence Option D is a perfect square
The perfect square trinomials from the given options are,
- [tex]y^2+20y+100[/tex]
- [tex]y^2+18y+81[/tex]
Thus the option a and d is the correct option.
What is perfect square trinomials?
A trinomial which is expressed as the square of the binomial equation is a perfect square trinomials.
- a) The trinomial given in the option 1 is,
[tex]y^2+20y+100[/tex]
Split the middle term to make the factor,
[tex]y^2+10y+10y+100\\y(y+10)+10(y+10)\\(y+10)(y+10)\\(y+10)^2[/tex]
As this trinomial can be expressed as the square of the binomial equation. Thus this is a perfect square trinomials.
- b) The trinomial given in the option 2 is,
[tex]y^2+25y+200[/tex]
The above trinomial can not be factorized.
As this trinomial can not be expressed as the square of the binomial equation. Thus this is not a perfect square trinomials.
- c) The trinomial given in the option 3 is,
[tex]y^2+6y+36\\[/tex]
The above trinomial can not be factorized.
As this trinomial can not be expressed as the square of the binomial equation. Thus this is not a perfect square trinomials.
- d) The trinomial given in the option 4 is,
[tex]y^2+18y+81[/tex]
Split the middle term to make the factor,
[tex]y^2+9y+9y+81\\y(y+9)+9(y+9)\\(y+9)(y+9)\\(y+9)^2[/tex]
As this trinomial can be expressed as the square of the binomial equation. Thus this is a perfect square trinomials.
Hence the perfect square trinomials from the given options are,
- [tex]y^2+20y+100[/tex]
- [tex]y^2+18y+81[/tex]
Thus the option a and d is the correct option.
Learn more about the perfect square trinomials here;
https://brainly.com/question/88561
