Question

select the polynomial that is a perfect square trinomial. 49x2 − 8x 16 4a2 − 10a 25 25b2 − 5b 10 16x2 −8x 1

Answer 1

`16x^2-8x+1=(4x-1)^2` is a perfect square trinomial.

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.

Answer 2

16x² - 8x + 1 = (4x)² - 2 · 4x · 1 + 1² =(4x - 1)²

Used: (a - b)² = a² -2ab + b²