Which Of The Following Expressions Are Perfect-square Trinomials? Check All Of The Boxes That Apply.

Answers

Perfect squares follow this pattern:

So, two terms must be perfect squares of two certain roots. If so, the remaining term must be twice their product. Let's analyse the trinomials one by one:

1) x^2 is the square of x. -64 is not a perfect square. So, the trinomial is not a perfect square.

2) 4x^2 is the square of 2x. 9 is the square of 3. The remaining term, 12x, is indeed twice their product. So, we have

3) x^2 is the square of x. 100 is the square of 10. The remaining term, 20x, is indeed twice their product. So, we have

4) x^2 is the square of x. 16 is the square of 4. The remaining term, 4x, is not twice their product (it's only the product of 4 and x, so it should be doubled). So, this trinomial is not a perfect square.

The answer is B and C

Remember that a perfect square trinomial can be factored into the form (a+b)^2
or (a-b)^2
Examples:
(x+2)(x+2) is a perfect sq trinomial --> x^2+4x+4
(x-3)(x-3) is a perfect sq trinomial --> x^2-6x+9
(x+2)(x-3) is not a perfect square trinomial because its not in the form (a+b)^2 or (a-b)^2

Now to answer your question,

for the first one, x^2-16x-64, you cannot factor it so it is not a perfect square trinomial

for the second one, 4x^2 + 12x + 9, you can factor that into (2x+3)(2x+3) = (2x+3)^2 so this is a perfect square trinomial

for the third one, x^2+20x+100 can be factored into (x+10)(x+10) so this is also a perfect square trinomial

for the fourth one, x^2+4x+16 cannot be factored so this is not a perfect square trinomial

Therefore, your answer is choices 2 and 3

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Which Of The Following Expressions Are Perfect-square Trinomials? Check All Of The Boxes That Apply.

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