Students can go through AP Board 8th Class Maths Notes Chapter 12 Factorisation to understand and remember the concepts easily.
AP State Board Syllabus 8th Class Maths Notes Chapter 12 Factorisation
→ Factorisation is a process of writing the given expression as a product of its factors.
→ A factor which cannot be further expressed as product of factors is an irreducible factor.
→ Expressions which can be transformed into the form:
a2 + 2ab + b2;
a2 – 2ab + b2;
a2 – b2 and x2 + (a + b)x + ab can be factorised by using identities.
→ If the given expression is of the form x2 + (a + b) x + ab, then its factorisation is (x + a)(x + b).
→ Division is the inverse of multiplication. This concept is also applicable to the division of algebraic expressions.
Gold Bach Conjecture:
→ Gold Bach found from observation that every odd number seems to be either a prime or the sum of a prime and twice a square.
Thus 21 = 19 + 2 or 13 + 8 or 3 + 18.
→ It is stated that up to 9000, the only exceptions to his statement are
5777 = 53 × 109 and 5993 = 13 × 641,
which are neither prime nor the sum of a primes and twice a square.