Expanding is the inverse transformation of factoring.
We need to perform expanding an expression (or some parts of an expression) in order to simplify the expression or reformulate a problem. In particular, many integrals are evaluated by expanding the integrands.

Let us consider a few examples.

1. If to remove the parentheses in the expression  (a - b)( a + b), then we obtain once again the formula for the difference between two squares:

    (a - b)( a + b) = a2 – b2.

2. Expanding the expression  (a + b) (a2 – a b + b2), we come back to the formula for the sum of two cubes:

   (a + b) (a2 – a b + b2) = a3 + b3.

3. Likewise,

   (a – b) (a2 + a b + b2) = a3 – b3,
   (a ± b)2 = (a2 ± 2 a b + b2),
   (a + b)3 = (a3 + 3 a2 b + 3 a b2 + b3).

4. If we represent the below expressions in expanded form and compare the results with the original forms, then no explanation required.

   

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