Which of the following does not factor as a perfect square trinomial? a. 16a^2-72a+81 b. 169x^2+26xy+y^2 c. x^2-18x-81 d. 4x^2+4x+1

The correct option is C.

Step-by-step explanation:

Lets solve each option one by one

A) 16a^2-72a+81

According to whole square formula:

a²-2ab+b² =(a-b)²

We have to take the square root of first and third term of each equation.

a² shows the first term = 16a^2

The square root of 16a^2 is 4a.. because 4 is the number which can be multiplied two times to give 16 and when we multiply a two times it gives us a².

b²  shows the third term = 81

The perfect square of 81 is 9.

2ab shows the middle term.

2ab = 2(4a)(9) = 72a

Thus we can factor it as a perfect square trinomial:

a²-2ab+b² =(a-b)²

16a²-72a+81 =(4a-9)²

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

a²+2ab+b² =(a+b)²

The square root of 169x² is 13x

Square root of y² is y

The middle term 26xy =2ab= 2(13x)(y)= 26xy

Thus we can factor it as a perfect square trinomial:

a²+2ab+b² =(a+b)²

169x^2+26xy+y^2 = (13x+y)²

C) x^2-18x-81

We can not factor it as a perfect square trinomial because the third term is negative.

D) 4x^2+4x+1

a²+2ab+b² =(a+b)²

The square root of 4x² is 2x

Square root of 1 is 1

The middle term 4x=2ab=2(2x)(1)= 4x

Thus we can factor it as a perfect square trinomial:

a²+2ab+b² =(a+b)²

4x^2+4x+1 = (2x+1)²

Thus the correct option is C