6-column table with 5 rows. The 1st column is labeled + x squared with entries +x, +x, +x, +x, +x. The 2nd column is labeled +x with entries +, +, +, +, +. The 3rd column is labeled +x with entries +, +, +, +, +. The 4th column is labeled +x with entries +, +, +, +, +. The 5th column is labeled +x with entries +, +, +, +, +. The 6th column is labeled +x with entries +, +, +, +, +.

Question

The algebra tiles represent the perfect square trinomial x2 + 10x + c.



What is the value of c?

c =

Answer 1

To represent the perfect square trinomial \(x^2 + 10x + c\) using algebra tiles, we start with the understanding that a perfect square trinomial can be expressed in the form \((x + a)^2\).

The general form of expanding \((x + a)^2\) is:

\[ (x + a)(x + a) = x^2 + 2ax + a^2 \]

From your trinomial \(x^2 + 10x + c\), we can compare coefficients:

• The coefficient of \(x\) in the trinomial, which is \(10\), gives us \(2a = 10\). Therefore, solving for \(a\):

\[ 2a = 10 \implies a = \frac{10}{2} = 5 \]

Now that we have \(a\), we can find \(c\) since it corresponds to \(a^2\):

\[ c = a^2 = 5^2 = 25 \]

So the value of \(c\) is:

\[ \boxed{25} \]