MCQ
Simplify $\Bigg(\frac{4\text{x}}{\text{y}}-\frac{7}{\text{z}}^2\Bigg)$using a suitable identity.
  • A
    $16\frac{\text{x}}{\text{y}}+56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
  • B
    $16\frac{\text{x}^2}{\text{y}^2}+56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
  • $16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
  • D
    $16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}-\frac{49}{\text{z}^2}$

Answer

Correct option: C.
$16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
C.  $16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
Solution:
Using $(a - b)^2 = a^2 - 2ab + b^2$
$\Bigg(\frac{4\text{x}}{\text{y}}-\frac{7}{\text{z}}\Bigg)^2=\Bigg(\frac{4\text{x}}{\text{y}}\Bigg)^2-2\times\frac{4\text{x}}{\text{y}}\times\frac{7}{\text{z}}+\Big(\frac{7}{\text{z}}\Big)^2$
$=16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$

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