Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers

Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-14. We provide step by step Solutions of Exercise / lesson-14 Factorization  for ICSE Class-8  RS  Aggarwal Mathematics.

Our Solutions contain all type Questions of Exe-14 A, Exe-14 B, Exe-14 C, Exe-14 D,  Exe-14 E(MCQ) with Notes to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.

Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-14

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Notes on Factorization

Exe-14 A,

 Exe-14 B,

 Exe-14 C,

 Exe-14 D,

(MCQ) Exe-14 E,

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Notes on Factorization

What is Factorisation?

An expression can be factorised into the product of its factors. These factors can be algebraic expressions, variables and numbers also.

When an expression is the product of two or more expressions, then each of the expressions is called a factor of the given expression.

When we factorise an algebraic expression, we write it as a product of irreducible factors. These factors may be numbers, algebraic variables or algebraic expressions.

Method of Common Factors

We factorise each term of the given algebraic expression as a product of irreducible factors and separate the common factors. Then, we combine the remaining factors in each term using the distributive law.

Factorisation By Regrouping Terms

Sometimes it so happens that all the terms in a given algebraic expression do not have a common factor; but the terms can be grouped in such a manner that all the terms in each group have a common factor. In doing so, we get a common factor across all the groups formed. This leads to the required factorisation of the given algebraic expression

Factorisation Using Identities

The following identities prove to be quite helpful in factorisation of an algebraic expression:
(a + b)² = a² + 2ab + b²
(a – b)² = a² – 2ab + b²
(a + b) (a – b) = a² – b²

Factors of the Form (x + a) (x + b)

(x + a) (x + b) = x² + (a + b) x + ab
To factorise an algebraic expression of the type x² + px + q, we find two factors a and b of q such that ab = q and a + b = p
Then, the given expression becomes
x² + (a + b) x + ab = x² + ax + bx + ab = x (x + a) + b (x + b) = (x + a) (x + b) which are the required factors.

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Exe-14 (A), Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions

Factorize :

Question 1:

6xy – 4xy

Question 2:

9bx² + 15b²x

Question 3:

……………………..

………………………

………………………

Question 20:

m(mx + ny)² + mn(mx + ny) + n(mx + ny)

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Exe-14 (B), Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions

Factorize :

Question 1:

5xy + 20x – 9y – 36

Question 2:

5ab – 10b – 7a + 14

Question 3:

…………………….

…………………….

…………………….

Question 22:

a²b² + b² + a² + 1

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Exe-14 (C), Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions

Factorize :

Question 1.

x² – 81

Question 2:

9a² – 25

Question 3:

………………………

………………………

………………………

Question 34:

Using the identity (a² – b²) = (a + b) (a – b) , evaluate each of the following :

(i) (82)²

(ii) (15.8)² – (9.2)²

(iii) (0.8)² – (0.2)²

(iv) {7 (3/4)}² – {2(1/4)}²

(v) {6 (4/11)}² – {4 (7/11)}²

(vi) 7(7.3 x 7.3 – 2.7 x 2.7)/(7.3 – 2.7)

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Exe-14 (D), Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions

Factorize :

Question 1.

x² + 18x + 81

Question 2.

a² – 14a  + 49

Question 3.

…………………..

……………………

…………………….

Question 27.

7 + 10 (x + y) – 8 (x + y)²

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MCQs Exe-14 (E), Factorization Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions

Multiple Choice Questions

Choose the correct option in each of the following ;

Question 1.

7x² – 63y² = ?

…………………….

Question 2:

(20 – 32x³) = ?
……………

Question 3:

…………………….

………………………

…………………………

Question 20.

3 + 23x – 8x² = ?
……………..

–: End of Factorization Class-8 RS Aggarwal Solutions :–

 

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