^{2}- B

^{2}is a special form of algebraic expression.

It is equal to (A + B)(A - B).

Many other expressions, like the cos2A = cos

^{2}A - sin

^{2}B,

can also be expressed in the special product form, that is,

cos2A = (cos A + sin A)(cos A - sin A).

But, how about A

^{2}+ B

^{2}?

Can it be expressed in the (A + B)(A - B) format?

Why not.

However we need to deviate a bit from the norm.

We need to know the imaginary "i" in complex number system.

Click

**here**for a review to it.

Since i

^{2}= -1, we can make use of this property for the special product A

^{2}+ B

^{2}.

Here it goes....

A

^{2}+ B

^{2}= A

^{2}- (i

^{2})(B

^{2})

Using the basic of Indices, it can be modified to,

A

^{2}-(iB)

^{2}

This becomes, therefore, (A + iB)(A - iB).

In summary,

A

^{2}- B

^{2}= (A + B)(A - B), and

A

^{2}+ B

^{2}= (A + iB)(A - iB).

The principles of the special product still holds regardless of the addition or subtraction operation between A square and B square.

Student: What an interesting twist is mathematics in this matter. Anything seems to be simple if we know the technique!

.

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