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8th Class Mathematics Algebraic Expressions Question Bank Algebraic Expressions and Identities

  • question_answer
    A T-shirt costs \[Rs.({{x}^{2}}-xy-{{y}^{2}})\] and a sweater costs \[Rs.({{x}^{2}}+8xy-2{{y}^{2}})\] and a jeans cost \[Rs.({{x}^{2}}-3xy+{{4}^{2}})\]. After buying these items Mohit paid \[Rs.{{(2x+y)}^{2}}\] to the cashier. How much amount Mohit receive from the cashier?

    A)  Rs. 0              

    B)  Rs. 2x

    C)  Rs. (x+y)       

    D)         Rs. 2y

    Correct Answer: A

    Solution :

    Cost of T-shirt\[={{x}^{2}}-xy-{{y}^{2}}\] Cost of sweater \[=2{{x}^{2}}+8xy-2{{y}^{2}}\] Cost of jeans\[={{x}^{2}}-3xy+4{{y}^{2}}\] Total Amount to be paid \[={{x}^{2}}-xy-{{y}^{2}}+2{{x}^{2}}+8xy-2{{y}^{2}}+{{x}^{2}}\] \[-3xy+4{{y}^{2}}\] \[=4{{x}^{2}}+4xy+{{y}^{2}}\] \[={{(2x+y)}^{2}}\]           \[(\because {{(a+b)}^{2}}={{a}^{2}}+2b+{{b}^{2}})\] Amount Mohit paid to the cashier\[={{(2x+y)}^{2}}\] \[\therefore \]Amount Mohit receives \[={{(2x+y)}^{2}}-{{(2x+y)}^{2}}=0\]


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