Answer:
x^2−18x+81
x^2+2x+1
Step-by-step explanation:
we know that
A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself
so
[tex]a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2[/tex]
Verify each case
case a) x^2−10x−25
we know that
[tex](x-5)^2=x^2-10x+25[/tex]
therefore
Is not a perfect square trinomial
case b) x^2−18x+81
we know that
[tex](x-9)^2=x^2-18x+81[/tex]
therefore
Is a perfect square trinomial
case c) x^2+2x+1
we know that
[tex](x+1)^2=x^2+2x+1[/tex]
therefore
Is a perfect square trinomial
case d) x^2+7x+49
we know that
[tex](x+3.5)^2=x^2+7x+12.25[/tex]
therefore
Is not a perfect square trinomial
