visual representation of algebra 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 ..

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..

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 - b) = a 2 - b 2 (x + a) (x + b) = x 2 + (a + b)x + ab. (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ac (a + b) 3 = a 3 + b 3 +..

Representation of a Function - A function can be represented by the following methods:A function can be represented by the following metho..

A function can be represented by the following methods: (i) An arrow diagram. (ii) Cartesian graph. (iii) Set-builder notatio..

(i) Roster form(i) Roster form (ii) Set builder form (iii) By tables (iv) Arrow diagram (v) By graphs (i) Roster form: The ordered pairs are listed, R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)} Where A = {1, 2, 3, 4, 5} and R means 'is twice' in A x A xRy means x = 2y. (i) x = 2y is called the def..

Rectangular axes - The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axis. The point of inte..

The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axi..

Conclusion - Linear inequations denote a user-friendly branch of mathematics which enables us to be very comfortable with the number line and properties of numbers.Linear inequations denote a user-friendly branch of mathematics which enables us to be very comfortable with the number line and proper..