Question

Simplify :  \[\frac{1 . 2 \times 1 . 2 \times 1 . 2 - 0 . 2 \times 0 . 2 \times 0 . 2}{1 . 2 \times 1 . 2 + 1 . 2 \times 0 . 2 + 0 . 2 \times 0 . 2}\]

Answer 1

The given expression is

 \[\frac{1 . 2 \times 1 . 2 \times 1 . 2 - 0 . 2 \times 0 . 2 \times 0 . 2}{1 . 2 \times 1 . 2 + 1 . 2 \times 0 . 2 + 0 . 2 \times 0 . 2}\]

Assume  a =1.2and . b= 0.2 Then the given expression can be rewritten as

 `(a^3  - b^3)/(a^2 +ab +b^2)`

Recall the formula for difference of two cubes

   `a^3 - b^3 = (a-b)(a^2 +ab +b^2)`

Using the above formula, the expression becomes

  `(a^3  - b^3)/(a^2 +ab +b^2) = ((a-b)(a^2 +ab+b^2))/(a^2 +ab+b^2)`

Note that both a , b is positive and unequal. So, neither `a^3 - b^3`nor any factor of it can be zero.

Therefore we can cancel the term `(a^2 + ab + b^2)`from both numerator and denominator. Then the expression becomes

`((a-b)(a^2 +ab+b^2))/(a^2 + ab +b^2) = a-b`

                                        ` = 1.2 - 0.2`

                                        ` = 1`