Education Technology

Factoring Special Cases

Activity Overview

Students explore geometric proofs for two factoring rules: a2 + 2ab + b2 = (a + b)2 and x2 – a2 = (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.

Key Steps

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    Students are given four figures: a square with side length a, two rectangles with side lengths a and b, and a square with side length b. Students should calculate the area of each of these and label each shape with its area.