Respuesta :
By definition, a Perfect square trinomial has the following form:
[tex]a^2\pm2ab+b^2[/tex]Perfect square trinomials can be expressed in Squared-binomial form, as following:
[tex](a\pm b)^2[/tex]In this case, you know that the first term of the Perfect square trinomial Tia wrote on the board, is:
[tex]4x^2[/tex]And the last term is:
[tex]25[/tex]Then you can identify that:
[tex]a^2=4x^2[/tex]Solving for "a", you get:
[tex]\begin{gathered} a=\sqrt[]{4x^2} \\ a=2x \end{gathered}[/tex]Notice that:
[tex]b^2=25[/tex]Solving for "b", you get:
[tex]\begin{gathered} b=\sqrt[]{25} \\ b=5 \end{gathered}[/tex]Knowing "a" and "b", you can write the following Squared-binomial:
[tex](2x+5)^2[/tex]And determine that the missing term is:
[tex]2ab=2(2x)(5)=20x[/tex]Therefore, the missing value is not a Perfect square, because it is not obtained by multiplying two equal Integers.
The answer is: Option B.
