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Factorization of the Expression of types a 4 + a 2 b 2 + b 4 or a 4 + 4b 4

 

 

Case 1: a 4 + a 2 b 2 + b 4 type expression

In such expression types we first try to convert one part of a given expression into  a^{2}+2(a)(b)+ b^{2} or  a^{2}-2(a)(b)+ b^{2} form and other part into a whole square — and finally the expression is converted into the form of   a^{2}- b^{2} and then factorization is done using factors form of  a^{2}- b^{2} as (a-b)(a+b)

 

Case 2: a 4 + 4b 4 type expression

In such type expression we convert a given expression to  a^{2}- b^{2} form by adding and subtracting last part of expression into the expression – and then get two whole square expression with subtraction sign between them.

 

Kindly see the questions for explanation and clarification.

 

 

 


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