Class 9 Mathematics | Punjab Curriculum and Textbook Board Syllabus 2025
The process of expressing an algebraic expression in terms of its factors is called factorization.
Example: \(5a + 5b = 5(a + b)\)
We use different terms to express the number of terms in an expression:
Monomial: An expression with only one term.
Examples: \(2x\), \(3y\)
Binomial: An expression with two terms.
Examples: \(2x + 3y\), \(x^2 - 4\)
Trinomial: An expression with three terms.
Examples: \(x^2 + 4x - 3\), \(2x^2 - 5x + 1\)
Polynomial: A broad category that includes all types of expressions with one or more terms.
The HCF of two or more algebraic expressions refers to the greatest algebraic expression which divides them without leaving a remainder.
We can find the HCF of given expressions by the following two methods:
The LCM of two or more algebraic expressions is the smallest expression that is divisible by each of the given expressions.
To find the LCM by factorization, we use the formula:
\(\text{LCM} = \text{Common factors} \times \text{Non-common factors}\)
The relationship between LCM and HCF can be expressed as follows:
\(\text{LCM} \times \text{HCF} = p(x) \times q(x)\)
Where,
\(p(x) = \text{1st polynomial}\)
\(q(x) = \text{2nd polynomial}\)
The square root of an algebraic expression refers to a value that, when multiplied by itself, gives the original expression.
Example: The square root of \(4a^2\) is \(\pm 2a\), because:
\(2a \times 2a = 4a^2\) and \((-2a) \times (-2a) = 4a^2\)
There are two methods for finding the square root of an algebraic expression: