mathematical expansions

Expansions - We shall discuss expansions of binomials and trinomi..

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 help us to avoid elab..

When pressure is applied on a gas, it contracts. Conversely, when pressure is released the gas expands. When the temperature is increased, the particles gain more energy, move faster and move away from each other. As a result the intermolecular attraction becomes less prominent. The volume of the ..

Summary - (a + b) (a - b) = a 2 - b 2 (x + a) (x + b) = x 2 + (a + b)x + ab. (a + b) 3 = a 3 + b 3 + 3ab (a + b) = a 3 + 3a 2 b + 3ab 2 + b 3..

Expansion of Matter - Matter expands on heating, i.e., solids, liquids and gases expand on heating. Let us consider expansion of solids: Three types of expansions are considered in case of solids. This classification is done according to the shape of the solid..

When length of a solid (rod) is much greater than its breadth and thickness, linear expansion or expansion in length is considered. Length of a rod increases on heati..

Liquids do not have a definite shape. They take the shape of the container. Thus, we can specify a liquid by its volume. Hence, we can speak of volume expansion only for liquids. Expansion of liquids is much greater than that of solid..

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 coefficient of superficial ..

Gases also expand on heating. Their volume expansion is very much greater than that of liquids. If a gas is heated at constant pressure, its volume increases and if a gas is heated at constant volume, its pressure increases due to expansion. Similarly, if we have to study ..

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 coefficient of superficial expansion is defined as the..