Answer:
The correct option is C.
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....