Students analyze various examples of perfect squares. A perfect square is an expression that is the result of multiplying something to itself. Students apply the distributive property repeatedly to expand perfect-square expressions given in factored form (MP8). The repeated reasoning allows them to generalize expressions of the form  as equivalent to .

Then students see that perfect squares can be handy for solving equations. Knowing that quadratic equations can be much more easily solved when one side is a perfect square and the other side is a number motivates students to transform expressions into that form. Recognizing the structure of a perfect square equips students to look for features that are necessary to complete a square (MP7).