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)
x2 + ax + bx + ab = (x + a) (x + b)
a2 + 2 ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
a2 – b2 = (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)
=x2 + bx + ax + ab = x2 + (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) = x2 + (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.