Answer:
\(16x^2-8x+1=(4x-1)^2\) is a perfect square trinomial.
Step-by-step explanation:
Given polynomials
\(49x^2-8x+16\\\\4a^2-10a+25\\\\25b^2-5b+10\\\\16x^2-8x+1\\\)
We have to choose the polynomial that is a perfect square trinomial.
- Trinomial is the polynomial having three terms.
- Perfect square trinomial are those polynomial having three terms and can be written as a perfect square that is in the form of \((a\pm b)^2\)
Consider the given polynomials
Since, all have three terms so, every given polynomial is trinomial.
and for perfect square consider \(16x^2-8x+1\)
This can be written as \(16x^2-8x+1=(4x)^2-2\cdot 4x\cdot 1+(1)^2\)
We know the algebraic identity, \((a-b)^2=a^2-2ab+b^2\)
On comparing a = 4x and b = 1
Thus, \(16x^2-8x+1=(4x-1)^2\)
Thus, \(16x^2-8x+1=(4x-1)^2\) is a perfect square trinomial.
