Practice Simplification Questions and Answers 2024

Rule	Description
1	An expression must be simplified by following defined order/sequence known as VBODMAS, which is given by: 1st step, V – Vineculum (line brackets)/Bar B – Brackets O – Of D – Division M – Multiplication A – Addition Last step, S – Subtraction There are four types of brackets given below. \[\bar \ \rightarrow\] Line/Bar \[( ) \ \rightarrow\] Simple or Small Bracket/open brackets \[\left\{\right\} \ \rightarrow\] Curly Brackets/Braces \[[ \ ] \ \rightarrow\] Square Brackets/Closed brackets These brackets must be solved in given order only.
2	\[a^2 + 2ab + b^2 = (a+b)^2\]
3	\[\frac{a^2-b^2}{a-b} =a+b\]
4	\[\frac{a^2-b^2}{a+b}=a-b\]
5	\[\frac{\left(a+b\right)^2+\left(a-b\right)^2}{\left(a^2+b^2\right)}=\] 2
6	\[\frac{a^3-b^3}{a^2-ab-b^2}\] \[=a+b\]
7	\[\frac{a^3-b^3}{a^2+ab+b^2}\] \[=a-b\]
8	\[\frac{1}{n\left(n+1\right)}+\frac{1}{n\left(n+1\right)\left(n+2\right)}+\frac{1}{n\left(n+2\right)\left(n+3\right)}+.....+\frac{1}{n\left(n+r-1\right)\left(n+r\right)}\] \[=\left(\frac{1}{n}-\frac{1}{n+1}\right)+\left(\frac{1}{n+1}-\frac{1}{n+2}\right)+\left(\frac{1}{n+2}-\frac{1}{n+3}\right)\] \[+.....+\left(\frac{1}{n+r-1}-\frac{1}{n+r}\right)\] \[=\left(\frac{1}{n}-\frac{1}{n+r}\right)\]
9	\[\frac{1}{n\left(n+2\right)}+\frac{1}{n\left(n+2\right)\left(n+4\right)}+\frac{1}{n\left(n+4\right)\left(n+6\right)}\] \[+.....+\frac{1}{\left(n+2r-2\right)\left(n+2r\right)}\] \[=\frac{1}{2}\left(\frac{1}{n}-\frac{1}{n+2r}\right)\]