Mental Squaring | (a - b) (a + b) approach

Of the 3 approaches in mental number squaring, this approach is more conceptual.

Have an overview of the 3 approaches here.

Principle: (a - b) (a + b) = a² - b²

But note that "b" is the difference to make the original number go to a 10's.
Example: 24 ==> a = 24 (original number), b = 4 (to make the original 24 go to 20)

However, note also, the principle has caused a new term "-b²" to appear.

Therefore to maintain the original squaring, we need to offset the new term with a "+b²".

The new formula to do mental squaring by the (a - b)(a + b) approach is:
a² = (a - b) (a + b) + b²

Example of usage: 34²

The 34² = (34 - 4)(34 + 4) + 4² letting b = 4.

Mentally multiplying (30)(38) can be easy ==> 1140 (click this link for method)

Finally, adding the b² = 4² = 16 ==> 1140 +16 = 1156 (ANSWER).

:-) Happy?

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