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6th Class Mathematics Algebra Question Bank Algebra

  • question_answer
    Read the following statements carefully and choose the correct answer. (i) The difference of the expressions \[3ab-2{{a}^{2}}-2{{b}^{2}}\] and \[5{{a}^{2}}-7ab+5{{b}^{2}}\] will be \[10ab-7{{a}^{2}}-7{{b}^{2}}\]  which is a trinomial. (ii) The sum of \[{{x}^{2}}+xy+{{y}^{2}}\] and \[2{{x}^{2}}+3xy\] gives an algebraic expression \[3{{x}^{2}}+4xy+{{y}^{2}}\].

    A)  (i) is true but (ii) is false.                 

    B)  (ii) is true but (i) is false.                

    C)  Both (i) and (ii) are true.

    D)  Neither (i) nor (ii) is true.

    Correct Answer: C

    Solution :

          (i) Difference\[=3ab-2{{a}^{2}}-2{{b}^{2}}-(5{{a}^{2}}-7ab+5{{b}^{2}})\] \[=(3ab+7ab-2{{a}^{2}}-5{{a}^{2}}-2{{b}^{2}}-5{{b}^{2}})\] \[=10ab-7{{a}^{2}}-7{{b}^{2}}\] \[10ab-7{{a}^{2}}-7{{b}^{2}}\] has three terms, so it is a trinomial. (ii) Sum of \[{{x}^{2}}+xy+{{y}^{2}}\] and \[2{{x}^{2}}+3xy\] is \[{{x}^{2}}+xy+{{y}^{2}}+2{{x}^{2}}+3xy\] \[=3{{x}^{2}}+4xy+{{y}^{2}}\].


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