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IM Alg1.7.8 Lesson: Rewriting Quadratic Expressions in Factored Form (Part 3)

Author:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

Find each product mentally.

Clare claims that is equivalent to and is equivalent to . Do you agree? Show your reasoning.

Use your observations from the first question and evaluate . Show your reasoning.

Check your answer by computing .

Is equivalent to ? Support your answer without a diagram.

Support your answer with a diagram.

Is (x+4)² equivalent to x²+4²? Support your answer, either with or without a diagram.

Explain how your work in the previous questions can help you mentally evaluate and .

Here is a shortcut that can be used to mentally square any two-digit number. Let’s take , for example.

  • 83 is .
  • Compute and , which give 6,400 and 9. Add these values to get 6,409.
  • Compute , which is 240. Double it to get 480.
  • Add 6,409 and 480 to get 6,889.
Try using this method to find the squares of some other two-digit numbers. (With some practice, it is possible to get really fast at this!) Then, explain why this method works.

Each row has a pair of equivalent expressions. Complete the table. If you get stuck, consider drawing a diagram. (Heads up: one of them is impossible.)

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