q4) Factorise

v)

a ^ 4 - 2 a^2 b^2 + b ^ 4

Answers (1)

We have,
             a ^ 4 - 2 a^2 b^2 + b ^ 4  =    a^{4} - a^{2}b^{2} - a^{2}b^{2} + b^{4}
                                               =     a^{2}(a^{2} - b^{2}) - b^{2}(a^{2} - b^{2})
                                               =   (a^{2} - b^{2}) (a^{2}-b^{2})                                              using \ a^{2}-b^{2} = (a-b)(a+b)
                                                =(a^{2} - b^{2})^{2}
                                                =((a - b)(a+b))^{2}
                                                 = (a - b)^{2}(a+b)^{2}

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