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Binomial formulas

The three binomial formulas (bi means the 2 letters a and b) are

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

(a + b)(a – b) = a2 – b2

 


Explanation

These formulas are frequently used to simplify calculations. They can be used from left to right and from right to left.

 


Example 1

In the picture are 2 squares and 4 right triangles.

You can calculate the area of the large square as

(a + b)(a + b) = a2 + 2ab + b2

and the area of the four triangles with

4 × ½ a b = 2ab

so that the area of the small square is equal to

(a + b)2 − 2ab = a2 + 2ab + b2 − 2ab = a2 + b2 = c2

This is the Pythagorean theorem.

 


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