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7th Class Mathematics Algebraic Expressions Question Bank Algebra

  • question_answer
    Consider the following statements: (i) The value of\[{{\left( 5x-3y \right)}^{2}}-{{\left( 5x+3y \right)}^{2}}\]when\[x=-1\]and\[y=\frac{1}{5}\]is 12. (ii) Algebraic identity used to solve \[{{\left( 25.732 \right)}^{2}}-{{\left( 15.732 \right)}^{2}}\]is \[\left( a-b \right)\left( a+b \right)\] (iii) Value of\[\left( x+4 \right)\left( x-4 \right)\left( {{x}^{2}}+16 \right)\]is\[{{x}^{2}}-64.\] Which of the above statement is/are true?

    A) only (i) and (iii)           

    B) only (ii) and (iii)

    C) only (i) and (ii)

    D)          (i), (ii) and (iii)

    Correct Answer: C

    Solution :

     \[\left[ {{(5x-3y)}^{2}}+{{(5x+3y)}^{2}} \right]\] Put \[x=-1,y=\frac{1}{5},\]we get \[{{\left[ 5(-1)-3\left( \frac{1}{5} \right) \right]}^{2}}-{{\left[ 5(-1)+3\left( \frac{1}{5} \right) \right]}^{2}}\] \[={{\left[ -5-\frac{3}{5} \right]}^{2}}-{{\left[ -5+\frac{3}{5} \right]}^{2}}\] \[=\left[ -5-\frac{3}{5}+5-\frac{3}{5} \right]\left[ -5-\frac{3}{5}-5+\frac{3}{5} \right]\] \[=\left( -\frac{6}{5} \right)(-10)=12\] (iii) \[\left( x+4 \right)\left( x-4 \right)\left( {{x}^{2}}+16 \right)\] \[=\left( {{x}^{2}}-16 \right)\left( {{x}^{2}}+16 \right)=\left( {{x}^{4}}-256 \right)\]


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