Question

For each expression, (a) complete the square to make a perfect square trinomial, and (b) write the result as a binomial squared:

Answer 1

Explanation

i)

Completing the square

To find the missing term, we proceed as follows:

$\begin{gathered} ax^2+bx+c\Rightarrow\text{ Standard form} \\ c=(\frac{b}{2})^2 \end{gathered}$

Then, we have:

$\begin{gathered} c^2-16c+? \\ ?=\left(\frac{16}{2}\right?^2 \\ ?=8^2 \\ ?=64 \end{gathered}$

Thus, the perfect square trinomial is:

$c^2-16c+64$

The perfect square trinomial as a binomial squared is:

$a^2-2ab+b^2=\lparen a-b)^2$

In this case, we have:

$undefined$

Answer