Notes On Factors of Algebraic Expressions - CBSE Class 8 Maths

Factorise an algebraic expression product of its factors.

The irreducible factor of an algebraic term is a factor of the term that cannot be further factorised. An algebraic expression written as the product of its irreducible factors is called the irreducible form of the term.

Factors
If an algebraic expression as the product of numbers or algebraic expressions then each of these numbers and expressions are called the factors.

Factorisation
Expressing an algebraic expression as the product of its factors is called the factorisation of the expression. This is the factor form of the expression.

The factors of an algebraic expression may be numbers or algebraic expression.

The basic methods to factorise an algebraic expression are:
     •  Identifying the common factors
     •  Regrouping the terms
     •  Using algebraic identities
     •  Factors of the form ( x + a)( x + b)

The basic identities used to factorise an algebraic expressions are:
     •  (a + b)2 = a2 + 2ab + b2
     •  (a - b)2 = a2 - 2ab + b2
     •  a2 - b2 = ( a + b)(a - b)
     •  (x + a)( x + b) = x2 + ( a + b)x + ab

Factorise 6xy + 3y.
= 6xy + 3y
= (2 × 3 × x × y ) + (3 × y)
= (3 × y) × (2 × x + 1)
= 3y(2x+1)  ← Factor form.

Summary

Factorise an algebraic expression product of its factors.

The irreducible factor of an algebraic term is a factor of the term that cannot be further factorised. An algebraic expression written as the product of its irreducible factors is called the irreducible form of the term.

Factors
If an algebraic expression as the product of numbers or algebraic expressions then each of these numbers and expressions are called the factors.

Factorisation
Expressing an algebraic expression as the product of its factors is called the factorisation of the expression. This is the factor form of the expression.

The factors of an algebraic expression may be numbers or algebraic expression.

The basic methods to factorise an algebraic expression are:
     •  Identifying the common factors
     •  Regrouping the terms
     •  Using algebraic identities
     •  Factors of the form ( x + a)( x + b)

The basic identities used to factorise an algebraic expressions are:
     •  (a + b)2 = a2 + 2ab + b2
     •  (a - b)2 = a2 - 2ab + b2
     •  a2 - b2 = ( a + b)(a - b)
     •  (x + a)( x + b) = x2 + ( a + b)x + ab

Factorise 6xy + 3y.
= 6xy + 3y
= (2 × 3 × x × y ) + (3 × y)
= (3 × y) × (2 × x + 1)
= 3y(2x+1)  ← Factor form.

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