Which of the following does not factor as a perfect square trinomial?

Option C. x^2-18x-81

Step-by-step explanation:

A. 16a^2-72a+81

x^2-2xy+y^2=(x-y)^2

x^2=16a^2→sqrt(x^2)=sqrt(16a^2)→x=sqrt(16) sqrt(a^2)→x=4a

y^2=81→sqrt(y^2)=sqrt(81)→y=9

2xy=2(4a)(9)→2xy=72a equal to the second term of the expression, then we can factor as a perfect square trinomial:

16a^2-72a+81=(4a-9)^2

B. 169x^2+26xy+y^2

a^2+2ab+b^2=(a+b)^2

a^2=169x^2→sqrt(a^2)=sqrt(169x^2)→a=sqrt(169) sqrt(x^2)→a=13x

b^2=y^2→sqrt(b^2)=sqrt(y^2)→b=y

2ab=2(13x)(y)→2ab=26xy equal to the second term of the expression, then we can factor as a perfect square trinomial:

169x^2+26xy+y^2=(13x+y)^2

C. x^2-18x-81

a^2+2ab+b^2=(a+b)^2

This expression does not factor as a perfect square trinomial because the third term is negative (-81).

D. 4x^2+4x+1

a^2+2ab+b^2=(a+b)^2

a^2=4x^2→sqrt(a^2)=sqrt(4x^2)→a=sqrt(4) sqrt(x^2)→a=2x

b^2=1→sqrt(b^2)=sqrt(1)→b=1

2ab=2(2x)(1)→2ab=4x equal to the second term of the expression, then we can factor as a perfect square trinomial:

4x^2+4x+1=(2x+1)^2