The image you uploaded is about completing a perfect square trinomial. Jeremiah is creating perfect square trinomials, and you are asked to move the correct term to complete each one.

A perfect square trinomial is of the form: $a^2 - 2ab + b^2 = (a - b)^2$ or $a^2 + 2ab + b^2 = (a + b)^2$

Looking at the expressions given:

1. $x^2 - 4x + \underline{\ }$
2. $x^2 + 20x + \underline{\ }$
3. $x^2 - 14x + \underline{\ }$

Let’s figure out the terms needed to complete the perfect square trinomial:

1. For $x^2 - 4x$: The coefficient of $x$ is $-4$. To make a perfect square, we take half of $-4$, which is $-2$, and then square it to get $4$. So the missing term is 4.

2. For $x^2 + 20x$: The coefficient of $x$ is $20$. Half of $20$ is $10$, and squaring it gives $100$. So the missing term is 100.

3. For $x^2 - 14x$: The coefficient of $x$ is $-14$. Half of $-14$ is $-7$, and squaring it gives $49$. So the missing term is 49.

Thus, the correct terms are:

• $x^2 - 4x + 4$
• $x^2 + 20x + 100$
• $x^2 - 14x + 49$

Would you like further clarification or additional help on this topic?

Here are five related questions you can explore next:

1. How can I expand a perfect square trinomial back into a binomial squared?
2. What is the process for factoring a perfect square trinomial?
3. How can I recognize if a trinomial is a perfect square trinomial?
4. Can a perfect square trinomial ever have a negative leading coefficient?
5. What other types of polynomials can be factored similarly to perfect square trinomials?

Tip: Practice recognizing the form of a perfect square trinomial: $x^2 + 2ab + b^2$ or $x^2 - 2ab + b^2$ to make completing the square easier.