fable 2 expansions

We shall discuss expansions of binomials, trinomials, Formulae 1. a 2 + b 2 = (a + b) 2 - 2ab 2. a 2 + b 2 = (a - b) 2 + 2ab 3. (a + b) 2 = (a - b) 2..

In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions h..

Expansions Summary - (a + b) 2 = a 2 + 2ab + b 2 (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 - 2ab + b 2 In the above two formulae the middle term = (a + b) (a..

Superficial Expansion - Expansion in area of a Laminar surface due to heating is known as superficial expansion. Let a 1 = area of a surface t 1 = its initial temperature a 2 = area of the surface after heating t 2 = final temperature The coefficien..

Assume a rod of material having a length L o at initial temperature T o . When the temperature changes by D T, the length changes by D L. Experiment shows that if D T is not too large (say, less than 100 o C or so), D L is directly proportional to D T. If two rods made of the same materia..

Increase in volume of a solid on heating is cubical expansion. Let V 1 = Initial volume at t 1 0 C V 2 = its volume at t 2 0 C (t 2 >t 1 ) Then increase in volume ' v' = v 2 -v 1 Increase in temperature ' t' = t 2 -t 1 The coefficient o..

Let the length of the rod increase to 'l 2 ' . Increase in length = (l 2 -l 1 ) = l Rise in temperature = (t 2 -t 1 ) 0 c = t. The ratio of increase in length to its original length per every degree rise in temperature is known as ' the coefficient of linear ..

Expansion of container with liquid In the figure L 1 represents the original level at the level of the liquid first falls to L 2 , because the container gets heat first. When the liquid gets heated, it expands much more than the container and its level rises to L 3 . We can only..

Heat..

Method of writing expansion for (a+b) n - Method of writing expansion for (a+b) n The first term in the expansion of (a + b) n is n C 0 a n b 0 . For the second term, the coefficient is taken as n C 1 , the power of 'a' is decreased by one and the power of 'b' is incre..