Respuesta :
Answer: [tex]4a^2 - 20a + 25 [/tex]
Step-by-step explanation:
A binomial [tex]ax^2+bx+c=0[/tex] is called perfect square trinomial
if [tex]b^2 = 4ac[/tex] is satisfied.
For [tex]49x^2 - 28x + 16[/tex]
a = 49, b = -28 and c = 16,
[tex](-28)^2=784[/tex]
[tex]4\times 49\times 16 =3136[/tex]
[tex]\implies (-28)^2\neq 4(49)(16)[/tex]
Thus, [tex]49x^2 - 28x + 16[/tex] is not a perfect square trinomial.
For [tex]4a^2 - 20a + 25 [/tex]
a = 4, b = -20 and c = 25,
[tex](-20)^2=400[/tex]
[tex]4\times 4\times 25 =400[/tex]
[tex]\implies (-20)^2\neq 4(4)(25)[/tex]
Thus, [tex]4a^2 - 20a + 25 [/tex] is a perfect square trinomial.
For [tex]25b^2 - 20b - 16[/tex]
a = 25, b = -20 and c = -16,
[tex](-20)^2=400[/tex]
[tex]4\times 25\times 16 =-1600[/tex]
[tex]\implies (-20)^2\neq 4(25)(16)[/tex]
Thus, [tex]25b^2 - 20b - 16[/tex] is not a perfect square trinomial.
For [tex]16x^2 - 24x - 9 [/tex]
a = 16, b = -24 and c = -9,
[tex](-24)^2=576[/tex]
[tex]4\times 16\times -9 =-576[/tex]
[tex]\implies (-24)^2\neq 4(16)(-9)[/tex]
Thus, [tex]16x^2 - 24x - 9 [/tex] is not a perfect square trinomial.
