Monday, 28 July 2008

Mental Squaring using (a + b)^2 approach

In this (a + b)2 approach to mental number squaring, the trick is to split the original number to one having 10's. After which, apply the (a + b)2 expansion to solve the multiplication.

Concept: Dealing with 10's is simpler than dealing with non-10's.

Principle: (a + b)2 = a2 + 2ab + b2

Example: 342

Step 1: Split the 34 into 30 + 4
Step 2: Replace the 342 by (30 + 4)2
Step 3: Expand Step 2. 302 + 2(30)(4) + 42

Mentally it is easy to do the 302 ==> 900.
Mentally it is also easy to do the 42 ==> 16.
It is also easy to mentally add up the above 2 results ==> 900 + 16 = 916.

Next, we need to multiply the centre term, which is the "2ab" part ==> 2(30)(4) ==> 240

Mentally we are able to add, the 916 to the last maths operation 240.
916 + 240 = 1156 (ANSWER).

Simple isn't it!

What we have done is to split the original number to a 10's and simplified the mental processing.
:-)

To see other ways to do number squaring mentally, click this link.

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