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SHORT REVISION ON ALGEBRAIC IDENTITIES.

 

SHORT REVISION ON ALGEBRAIC IDENTITIES.

As you probably know “An Algebraic identity is an algebraic equation that is true for all values of the variables occurring in it.” These Identities play a vital role in any algebraic or mathematical calculation.

So, this post is made for the short revision of the Algebraic Identities. Some of these are :

·        (x + y)2 = x2 + 2xy + y2
·        (x - y)2 = x2 - 2xy + y2
·        x2 – y2 = (x + y) (x – y)
·        (x + a) (x + b) = x2 + (a + b)x + ab
·        (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
·        (x + y)3 = x3 + y3 + 3xy (x + y) 
·        (x – y)3 = x3 – y3 – 3xy(x – y)
·        x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx)
·        x3 + y3 = (x + y)(x2 – xy + y2)
·        x3 - y3 = (x - y)(x2 + xy + y2)

Some advanced Algebraic Identities :

·        x2 + y2 = (x - y)2 + 2xy
·        (x + y)2 = (x - y)2 + 4xy
·        (x - y)2 = (x + y)2 - 4xy
·        x4 – y4 = (x2 + y2)(x + y)(x - y)
·       x8 – y8 = (x4 + y4)(x2 + y2)(x + y)(x - y)
·        (x + y + z)3 = x3 + y3 + z3 + 3(x + y)(y + z)( z + x)

These are the algebraic identities that are used mostly in the calculation.


Recommended -

Short trick to calculate the square of two digits Numbers.

Short trick to multiply any two digits Number by 11.

Short trick to multiply any two digits Numbers.

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