Verified Answer :
Answer:
Option A :\(y^{2} +20y+100\)
Option D: \(y^{2} +18y+81\)
Step-by-step explanation:
To Find: Which trinomials are perfect square trinomials?
option A :\(y^{2} +20y+100\)
Factorizing:
\(y^{2} +10y+10y+100\)
\(y(y+10)+10(y+10)\)
\((y+10)(y+10)\)
\((y+10)^{2}\)
Hence Option A is perfect square
Option B : \(y^{2} +25y+200\)
Since this cannot be factorized
Hence not a perfect square
Option C: \(y^{2} +6y+36\)
Since this cannot be factorized
Hence not a perfect square
Option D: \(y^{2} +18y+81\)
\(y^{2} +9y+9y+81\)
\(y(y+9)+9(y+9)\)
\((y+9)(y+9)\)
\((y+9)^{2}\)
Hence Option D is a perfect square
The perfect square trinomials from the given options are,
- \(y^2+20y+100\)
- \(y^2+18y+81\)
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,
\(y^2+20y+100\)
Split the middle term to make the factor,
\(y^2+10y+10y+100\\y(y+10)+10(y+10)\\(y+10)(y+10)\\(y+10)^2\)
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,
\(y^2+25y+200\)
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,
\(y^2+6y+36\\\)
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,
\(y^2+18y+81\)
Split the middle term to make the factor,
\(y^2+9y+9y+81\\y(y+9)+9(y+9)\\(y+9)(y+9)\\(y+9)^2\)
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,
- \(y^2+20y+100\)
- \(y^2+18y+81\)
Thus the option a and d is the correct option.
Learn more about the perfect square trinomials here;
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