Each diagram represents the square of an expression or a perfect square.

1. Complete the cells in the last table.
2. How are the contents of the three diagrams alike? This diagram represents . Describe your observations about cells 1, 2, 3, and 4.

   	term_1	term_2
   term_1	cell 1	cell 2
   term_2	cell 3	cell 4

3. Rewrite the perfect-square expressions , , and in standard form: .
4. How are the , , and of a perfect square in standard form related to the two terms in ?

Solve each equation.

Explain or show why the product of a sum and a difference, such as , has no linear term when written in standard form.

To solve the equation , Han first expanded the squared expression. Here is his incomplete work:

1. Complete Han’s work, and solve the equation.

2. Jada saw the equation and thought, “There are two numbers, 2 and -2, that equal 4 when squared. This means is either 2 or -2. I can find the values of from there.”

   Use Jada’s reasoning to solve the equation.

3. Can Jada use her reasoning to solve ? Explain your reasoning.

Given triangle , angle is 90 degrees, and angle is 45 degrees. Side is 3 feet. How long is side ?