Page 259 - ICSE Math 6

Terms A constant/a variable/a combination of constants and variables

Like terms Terms with the same literal factors 2x, –11x and 230x

Unlike terms Terms with different literal factors 5y, –11m and pq

Constant terms A term with no variable –7, 21, 315 and so on.

In a term, constant is known as the numerical factor.
Numerical Literal
Factor Factor
In a term, variables are known as the literal factors.

Algebraic Expressions Monomial: With one non-zero term.
With powers
A collection of one or more of variables in Binomial: With two non-zero terms.
terms combined together by whole numbers Trinomial: With three non-zero terms.
addition or subtraction. Polynomial: With finite non-zero terms.

OPERATIONS ON ALGEBRAIC EXPRESSIONS

Substitution Example
The method of finding the For x = 2,
value of an expression by
substituting the values of the 2x + 1 = 2(2) + 1
variables in the expression. = 1

Removing a Bracket

When there is a ‘+’ sign Remove the bracket and retain the signs of each term inside
before the bracket. the bracket as it is. For e.g.: 3 + (x + 2y – 7) = 3 + x + 2y + 7
When there is a ‘–’ sign Remove the bracket and change the signs of each term inside
before the bracket. the bracket. For e.g.: 3 – (x + 2y – 7) = 3 – x – 2y + 7

LINEAR EQUATIONS IN ONE VARIABLE

Equation A mathematical statement which shows the equality of two expressions.

Linear Equation An equation which consists of variables with highest power 1.

Linear Equation in One Variable A linear equation with only one variable.

x = y x = y Solution of a Linear Equation
⇒ x + a = y + a ⇒ x – a = y – a
Properties of Value of variable which
an Equation satisfies the given equation.
x = y x = y and a ≠ 0
⇒ x × a = y × a ⇒ x ÷ a = y ÷ a

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