Algebraic Identity - Square of difference of Binomial


 
 
Concept Explanation
 

Algebraic Identity - Square of difference of Binomial

Algebraic Identity - Square of Difference of Binomial : -

small (a-b)^{2}=a^{2}-2ab+b^{2}

You can easily get this identity by multiplying binomial a-b with itself,

small (a-b)^{2}=(a-b)(a-b)

                 small = a(a-b)-b(a-b)

                small = a^2-ab-ba+b^{2}

                small =a^{2}-2ab+b^{^{2}}

Similarly ,small (b-a)^{2}can also be found.

             small (b-a)^{2}=b^{2}-2ba+a^{2}

                              small =a^{2}-2ab+b^{2}

                              small (b-a)^{2}=(a-b)^{2}

  • Identity -II can also be considered as a special case of identity I when'b' is replaced by '-b'.
  •          Identity -I is :

    small (a+b)^{2}=a^{2}+2ab +b^{2}

    Replace 'b' by ' -b'in the above identity :

    small (a+(-b)^{2})=a^{^{2}}+2atimes (-b)+(-b^{2})

    small (a-b^{2})=a^{2}-2ab+b^{2} which is identity -II.

    Example:- Find small (2x-3y)^{2}using identity -II .

    Solution:  small (2x-3y)^{2}=(2x)^{2}-2times 2xtimes 3y+(3y)^{2}

                                         small = 4x^{2}-12xy +9y^{2}

    Example: Evaluate small (99)^{2}using identity -II.

    Solution: small (99)^{2}=(100-1)^2=100^{2}-2times 100times 1+1

                 small =10000 -200 +1 =9801     

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    large frac{(856+167)^2+(856-167)^2}{856X856+167X167} is equal to

    Right Option : B
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    Explanation
    Question : 2

    frac{55X55-2X25X55+25X25}{(30)^2}=? 

    Right Option : D
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    Explanation
    Question : 3

    left (frac{1}{2}x-frac{1}{5}yright)left(frac{1}{2}x-frac{1}{5}yright)=_________________

    Right Option : D
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