# Simplification

Pratice Simplification Questions and answers.

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.

1. $\bar \ \rightarrow$ Line/Bar
2. $( ) \ \rightarrow$ Simple or Small Bracket/open brackets
3. $\left\{\right\} \ \rightarrow$ Curly Brackets/Braces
4. $[ \ ] \ \rightarrow$ 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

$\frac{1}{n\left(n+2\right)}+\frac{1}{n\left(n+2\right)\left(n+4\right)}+\frac{1}{n\left(n+4\right)\left(n+6\right)}$

$+.....+\frac{1}{\left(n+2r-2\right)\left(n+2r\right)}$

$=\frac{1}{2}\left(\frac{1}{n}-\frac{1}{n+2r}\right)$