STD IX – ALGEBRA – (Online)

EXPANSIONS

Expansion is the act of expanding, mathematically speaking, it is removing all the brackets present in the expression. Usually in math, we encounter a few expression where they place two sets of two terms, both in brackets side by side like this (a+b)(a-b).This requiring removing of brackets and simplification.

FACTORIZATION

Factorisation or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

For example, the number 15 factors into primes as 3 × 5, and the polynomial x^2 − 4 factors as (x − 2) (x + 2).

In all cases, a product of simpler objects is obtained. It is actually the opposite of expansion.

SIMULTANEOUS LINEAR EQUATION

System of simultaneous linear equations

A pair of linear equations in the same two variables forms a system of simultaneous linear equations. They are satisfied by the same pair of values of the two variables. Two linear equations can have either only one solution, no solution or infinite solutions.

INDICES

The index of a number is the number which shows how many times that number has occurred in the term as a repeated factor.

aⁿ implies that the number a is multiplied by itself n number of times, where n is a positive integer. ‘a’ is called the base and n is called the index or exponent or power.

LOGARITHMS

The logarithm of a positive real number b with respect to a positive base number a is the power n  of a to which a must be raised to obtain.