Q&A #15927

Algebraic identities

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From: Marielouise (for Teacher2Teacher Service)
Date: Sep 21, 2005 at 22:13:15
Subject: Re: Algebraic identities


Before one can memorize something and be able to apply the idea, it is
necessary to understand the underlying concept.

Have the student work out several long multiplications of (a + b) ^2 and (a +

Look at the process of what is happening. The student can always multiply the
long way. The motivation, after understanding what is happening, is to try to
"speed up" the calculation because each time you multiply the binomials it
results in the same format.

Some students are helped by seeing a visualization. (a + b)^2 is looking at
the portions of a square made up of a side (a + b). There is a square whose
area is a^2 and a square whose area is b^2.  There are also two rectangles
whose area is ab. Hence, the result  a^2 + 2ab + b^2.

The visualization of (a + b)^3 is much more difficult because you are dealing
with a cube each of whose edges are (a + b). There are 8 pieces within the
cube: an a^3, a b^3, three a^2b and three ab^2-

It might be worth it for the students to see a cube of styrofoam that is cut
into all of the eight pieces.

I wish you well teaching this.

Marielouise, for the T2T service

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