which are perfect square trinomials? select two options.\nx² - 9\nx² - 100\nx² - 4x + 4\nx² + 10x + 25\nx² +…

Explanation:

Step1: Recall the formula for perfect - square trinomial

The formula for a perfect - square trinomial is (a^{2}\pm2ab + b^{2}=(a\pm b)^{2}).

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

For (x^{2}-4x + 4), let (a = x) and (b = 2). Then (2ab=2\times x\times2 = 4x). So (x^{2}-4x + 4=(x - 2)^{2}).

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

For (x^{2}+10x + 25), let (a=x) and (b = 5). Then (2ab=2\times x\times5=10x). So (x^{2}+10x + 25=(x + 5)^{2}).

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

(x^{2}-9=x^{2}-3^{2}) is a difference of squares ((a^{2}-b^{2}=(a + b)(a - b))), not a perfect - square trinomial.

Step5: Analyze (x^{2}-100)

(x^{2}-100=x^{2}-10^{2}) is a difference of squares ((a^{2}-b^{2}=(a + b)(a - b))), not a perfect - square trinomial.

Step6: Analyze (x^{2}+15x + 36)

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

Answer:

(x^{2}-4x + 4) and (x^{2}+10x + 25)