Question

Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply.

Answer 1

Perfect squares follow this pattern:

$(a\pm b)^2 = a^2\pm 2ab+b^2$

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

$4x^2 +12x +9 = (2x+3)^2$

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

$x^2 +20x +10 = (x+10)^2$

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.

Answer 2

The answer is B and C