Algebra I
View Activity ArchivesActivity:
Factoring Special Cases
Posted on Mar 20, 2008
Topic: Quadratic Functions & Equations
In this activity, students explore geometric proofs for two factoring rules: a^2+2ab+b^2=(a+b)^2 and x^2–a^2=(x–a)(x+a). Given a set of shapes whose combined areas represent the left-hand expression, they manipulate them to create rectangles whose areas are equal to the right-hand expression.
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Activity Key Steps:
In Problem 1, students investigate factoring a perfect-square trinomial by considering four figures: a square with side length a, two rectangles with side lengths a and b, and a square with side length b. Students will calculate the area of each of these and label each shape with its area.
Students rearrange the shapes to form a square.
They will find that each side of the square is made up of two pieces, one with length a and one with length b, so the length of each side is the sum of these, a + b.
In Problem 2, students prove the rule for factoring a difference of squares. They are given a square with side length m and a square with side length n. They should label each square with its area.
Students will then manipulate the squares to show removing the smaller from the larger.
Students next transform the gray L-shape that remains into a long rectangle with the same area. They then compare the areas.
At the end of this activity, students will know and understand the concept when factoring special cases. They will be able to express a trinomial square as a binomial square. They will also be able to express a difference of squares and display as a difference of areas.