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harkovskaia [24]
3 years ago
13

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

Mathematics
2 answers:
Evgesh-ka [11]3 years ago
8 0
16x² - 8x + 1 = (4x)² - 2 · 4x · 1 + 1² =(4x - 1)²

Used: (a - b)² = a² -2ab + b²
Sav [38]3 years ago
5 0

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.

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