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

User Thomas Lindauer
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1 Answer

12 votes
12 votes

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

User Freiksenet
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