This GSEB Class 8 Maths Notes Chapter 14 Factorisation covers all the important topics and concepts as mentioned in the chapter.

## Factorisation Class 8 GSEB Notes

→ The method of writing a given algebraic expression as the product of two expressions is known as the factorisation of the Expressions.

→ ax + ay + az = a (x + y + z)

x^{2} + ax + bx + ab = (x + a) (x + b)

a^{2} + 2 ab + b^{2} = (a + b)^{2}

a^{2} – 2ab + b^{2} = (a – b)^{2}

a^{2} – b^{2} = (a – b) (a + b)

→ 1 is a factor of each term.

→ Common methods of factorisation:

- By finding common factors
- Rearranging terms
- By getting idea of proper identities
- Factorisation by splitting the middle term.

(x + a) (x + b)

= x (x + b) + a (x + b)

=x^{2}+ bx + ax + ab = x^{2}+ (a + b) x + ab

→ Middle term – (a + b)x = (sum of constants) x,

and last term = ab = Product of constants

i. e., (x + a) (x + b) = x^{2} + (sum of constants) x + product of constants

→ In division of a polynomial by a monomial, either carry out the division by dividing each term of the polynomial by the monomial or by the common factor method.

→ In division of polynomial by a polynomial, factorise both the polynomials and cancel their common factors.

→ Tips to find errors from algebraic expression:

- Check sign of each term
- Addition and subtraction of like terms only
- Exponents of variables change only during multiplication and division of terms.
- Use identity where it is possible.