Example Question 7

Example corresponding to question 7 in algebra_4.

Example 1


$(3a - \dfrac{1}{3a})^2$ is equivalent to

  1. $9a^2+\dfrac{1}{9a^2}$


  2. $9a^2-\dfrac{1}{9a^2}$


  3. $9a^2-2+\dfrac{1}{9a^2}$


  4. $9a^2+2+\dfrac{1}{9a^2}$
  5. 1

Solution


  1. The given expression is the square of a difference: $(x-y)^2=x^2-2xy+y^2$

    Apply it to the given expression with $x = 3a$ and $y=\dfrac{1}{3a}$

    $(3a - \dfrac{1}{3a})^2=(3a)^2-2(3a)(\dfrac{1}{3a})+(\dfrac{1}{3a})^2$

  2. Simplify the middle term as follows:

    $2(3a)(\dfrac{1}{3a}) = 2\dfrac{3a}{3a}=2\dfrac{\colorcancel{red}{3a}}{\colorcancel{red}{3a}}=2$

    Hence

    $(3a - \dfrac{1}{3a})^2=9a^2-2+\dfrac{1}{9a^2}$

    Answer C