Question

Fill in the blank with a number to make the expression a perfect square.Y^2+16y +

Answer 1

You can identify that the expression is a polynomial and its degree is 2.

As you can see in the exercise, it has the following form:

$ax^2+bx^{}+c$

You know two terms of the expression:

$y^2+16y$

By definition, a Perfect square expression is an expression that can be factored in the form of the product of two Binomials:

$\begin{gathered} a^2+2ab+b^2=(a+b)(a+b) \\ \\ a^2-2ab+b^2=(a-b)(a-b) \end{gathered}$

Therefore, knowing the two terms of the expression given, you can set up that:

$\begin{gathered} a=y \\ \\ 2ab=(2)(y)(8)=16y \end{gathered}$

Then:

$b^2=(8)^2=64$

The answer is:

$64$