Respuesta :
Perfect squares follow this pattern:
[tex] (a\pm b)^2 = a^2\pm 2ab+b^2 [/tex]
So, two terms must be perfect squares of two certain roots. If so, the remaining term must be twice their product. Let's analyse the trinomials one by one:
1) x^2 is the square of x. -64 is not a perfect square. So, the trinomial is not a perfect square.
2) 4x^2 is the square of 2x. 9 is the square of 3. The remaining term, 12x, is indeed twice their product. So, we have
[tex] 4x^2 +12x +9 = (2x+3)^2 [/tex]
3) x^2 is the square of x. 100 is the square of 10. The remaining term, 20x, is indeed twice their product. So, we have
[tex] x^2 +20x +10 = (x+10)^2 [/tex]
4) x^2 is the square of x. 16 is the square of 4. The remaining term, 4x, is not twice their product (it's only the product of 4 and x, so it should be doubled). So, this trinomial is not a perfect square.
The expression that shows perfect-square trinomials are [tex]4x^2+12x+9[/tex] and [tex]x^2+20x+100[/tex] and this can be determined by using factorizing the given polynomials.
Check all the given polynomials in order to determine which expression is a square polynomial.
A) [tex]x^2-16x-64[/tex]
This polynomial is not a perfect square because the polynomial is not factorized further.
B) [tex]4x^2+12x+9[/tex]
[tex]=4x^2+6x+6x+9[/tex]
= 2x(2x + 3) + 3(2x + 3)
[tex]=(2x+3)^3[/tex]
So, this polynomial is a perfect square.
C) [tex]x^2+20x+100[/tex]
[tex]=x^2+10x+10x+100[/tex]
[tex]=(x+10)(x+10)[/tex]
[tex]=(x+10)^2[/tex]
So, this polynomial is a perfect square.
D) [tex]x^2+4x+16[/tex]
This polynomial is not a perfect square because the polynomial is not factorized further.
For more information, refer to the link given below:
https://brainly.com/question/3655826
