91Ó°ÊÓ

According to BODMAS rule of simplification, at first the bracket operation must be completed followed division, by multiplication, addition and finally subtraction.

The expression $b(c−d)−e$can be written as

$\begin{array}{l}b(c−d)÷e=\left[\right(b×c)−(b×d\left)\right]÷e\\ \text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}=(bc−bd)÷e\\ \text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}=\frac{(bc−bd)}{e}\end{array}$

Two expressions are said to be equivalent if their values equal respectively.

Now, the simplification of $\left(30+17\right)×10$can be obtained as:

$\begin{array}{c}\left(30+17\right)×10\\ =47×10\\ =470\end{array}$

Similarly, the simplification of $\left(10×30\right)+\left(10×17\right)$can be obtained as:

$\begin{array}{c}\left(10×30\right)+\left(10×17\right)\\ =300+170\\ =470\end{array}$

Hence, it can be seen that the values of both the expressions are equivalent.