Question

Which trinomials are perfect square trinomials? Select each correct answer. a.y2+20y+100 b.y2+25y+200 c.y2+6y+36 d.y2+18y+81

Answer 1

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

Answer 2

Answer: A & D
A can be factored into (y + 10)^2
D can be factored into (y + 9)^2