Have an overview of the 3 approaches

**here**.

Principle: (a - b) (a + b) = a

^{2}- b

^{2}

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 "-b

^{2}" to appear.

Therefore to maintain the original squaring, we need to

__the new term with a "+b__

**offset**^{2}".

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

**a**

^{2}= (a - b) (a + b) + b^{2}Example of usage: 34

^{2}

The 34

^{2}= (34 - 4)(34 + 4) + 4

^{2}letting b = 4.

Mentally multiplying (30)(38) can be easy ==>

**1140**(click this

**link**for method)

Finally, adding the b

^{2}= 4

^{2}= 16 ==>

**1140**+16 = 1156 (ANSWER).

:-) Happy?

.

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