which are perfect square trinomials? select two options.\n$x^{2}-9$\n$x^{2}-100$\n$x^{2}-4x + 4$\n$x^{2}+10x…

Explanation:

Step1: Recall perfect - square trinomial formula

A perfect - square trinomial is of the form (a^{2}+2ab + b^{2}=(a + b)^{2}) or (a^{2}-2ab + b^{2}=(a - b)^{2}).

Step2: Analyze (x^{2}-4x + 4)

Here, (a=x), (2ab = 4x), so (2b = 4) (since (a=x)), then (b = 2), and (x^{2}-4x + 4=(x - 2)^{2}).

Step3: Analyze (x^{2}+10x + 25)

Here, (a=x), (2ab=10x), so (2b = 10) (since (a=x)), then (b = 5), and (x^{2}+10x + 25=(x + 5)^{2}).

Step4: Analyze (x^{2}-9) and (x^{2}-100)

(x^{2}-9=(x + 3)(x - 3)) and (x^{2}-100=(x+10)(x - 10)), they are difference - of - squares, not perfect - square trinomials.

Step5: Analyze (x^{2}+15x + 36)

For (x^{2}+15x + 36), if it is of the form (a^{2}+2ab + b^{2}) with (a=x), then (2b = 15), (b=\frac{15}{2}), and (b^{2}=\frac{225}{4}\neq36), so it is not a perfect - square trinomial.

Answer:

C. (x^{2}-4x + 4), D. (x^{2}+10x + 25)