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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

 

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Explanation

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

 

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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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