Upto second order, paper folding will be of use. For example, (a+b+c)^2 can be explained by
creating a paper folding similar to
The higher order needs to be explained with written materials using the logic of second
order. Sufficient practice must be given in enabling the child to recollect all the identities
once they are taught. Some general principles may help to understand. Take for example
(a+b)^3.
Here the products are of three types - purely involving ‘a’, purely involving ‘b’ and a
product of ‘a’ and ‘b’ with different combinations. Let the child be helped to understand
a pattern in the expansion.
(a+b)^2 = a^3 + 3a^2 b + 3ab^2 + b^3In the third order, the sum of the powers of the products should necessarily be 3. That is
3a^2 b is a product of a & b, with the power of ‘a’ as 2 and power of b as ‘ 1 ’. Moreover, the
power of the first variable decreases in the subsequent place values. That is when the
power of one variable ‘descends’, the other value ‘ascends’. That is why the third number
is 3ab^2 , one power less than the previous one in the case of ‘a’ and one more in the case of
‘b’. This logic can be applied in (a+b)^2 = a^2 +2ab+b^2 , etc.
a
bcab c