| Topic Included: | Formulas, Definitions & Exmaples. |
| Main Topic: | Quantitative Aptitude. |
| Quantitative Aptitude Sub-topic: | Simplification Aptitude Notes & Questions. |
| Questions for practice: | 10 Questions & Answers with Solutions. |
For simplifying a question you must follow the sequence. Remember the word "VBODMAS". $$ 1 \longrightarrow V \longrightarrow {Vinculum \ or \ Bar \ (\bar{N})} $$ $$ 2 \longrightarrow B \longrightarrow Brackets, \ (1), \left\{2\right\}, [3] $$ $$ O \longrightarrow {of} $$ $$ 3 \longrightarrow D \longrightarrow {Division (\div)} $$ $$ 4 \longrightarrow M \longrightarrow {Multiplication (\times)} $$ $$ 5 \longrightarrow A \longrightarrow {Addition (+)} $$ $$ 6 \longrightarrow S \longrightarrow {Subtraction (-)} $$
Under the Vinculum or bar \((\bar{N})\), Here N is any number
Under the brackets, solve brackets as numbered inside the brackets \((1), \left\{2\right\}, [3]\).
Example(1): \(\left[(6)^3 \times (3)^2\right] \div (2)^3 = ?\)
Solution: $$ \left[(6)^3 \times (3)^2\right] \div (2)^3 $$ $$ \left[216 \times 9\right] \div 8 $$ $$ 1944 \div 8 = 243 $$
Example(2): \(216 \div 36 + 4 - 2 = ?\)
Solution: $$ 216 \div 36 + 4 - 2 $$ $$ 6 + 4 - 2 $$ $$ 10 - 2 = 8 $$
Example(3): \(\left[{(20)^3 \div (8 + 2)^2 \times 2}\right] + 12 - 8 = ?\)
Solution: $$ \left[{(20)^3 \div (8 + 2)^2 \times 2}\right] + 12 - 8 $$ $$ \left[{8000 \div 100 \times 2}\right] + 12 - 8 $$ $$ \left[{80 \times 2}\right] + 12 - 8 $$ $$ \left[160\right] + 12 - 8 $$ $$ 160 + 12 - 8 $$ $$ 172 - 8 = 164 $$
$$ (a + b)^2 = a^2 + 2ab + b^2 $$ $$ (a - b)^2 = a^2 - 2ab + b^2 $$ $$ (a^2 + b^2) = (a - b)^2 + 2ab $$ $$ (a^2 - b^2) = (a + b) \ (a - b) $$ $$ (a + b)^3 = a^3 + b^3 + 3ab \ (a + b) $$ $$ (a - b)^3 = a^3 - b^3 - 3ab \ (a - b) $$ $$ (a^3 + b^3) = (a + b) \ (a^2 + b^2 - ab) $$ $$ (a^3 - b^3) = (a - b) \ (a^2 + b^2 + ab) $$