ICSE Class 8 Maths Selina Solutions Chapter 13 Factorisation

Factorisation is a fundamental process in algebra where we break down algebraic expressions into simpler factors. This simplification helps in solving equations, understanding relationships between variables, and making calculations more manageable. Here's a detailed explanation with examples of common factorisation methods:

Finding Common Factors :

• Example : Factorise $6x+9y$ .
• Solution : First, identify the common factor. In this case, it's 3. $6x+9y=3(2x+3y)$

Grouping Terms :

• Example : Factorise $ax+ay+bx+by$ .
• Solution : Group the terms with common factors together. $ax+ay+bx+by=a(x+y)+b(x+y)=(a+b)(x+y)$

Difference of Squares :

• Example : Factorise x2−9x^2 - 9 x 2 − 9 .
• Solution : Recognize it as a difference of squares and apply the formula. x2−9=(x−3)(x+3)x^2 - 9 = (x - 3)(x + 3) x 2 − 9 = ( x − 3 ) ( x + 3 )

Perfect Square Trinomials :

• Example : Factorise x2+6x+9x^2 + 6x + 9 x 2 + 6 x + 9 .
• Solution : Check if it can be written as a perfect square. x2+6x+9=(x+3)2x^2 + 6x + 9 = (x + 3)^2 x 2 + 6 x + 9 = ( x + 3 ) 2

Factoring by Grouping :

• Example : Factorise ax2+bx+ay+byax^2 + bx + ay + by a x 2 + b x + a y + b y .
• Solution : Group terms and find common factors within each group. ax2+bx+ay+by=a(x2+y)+b(x+y)=(ax+b)(x+y)ax^2 + bx + ay + by = a(x^2 + y) + b(x + y) = (ax + b)(x + y) a x 2 + b x + a y + b y = a ( x 2 + y ) + b ( x + y ) = ( a x + b ) ( x + y )

Understanding these factorisation methods is important as they form the basis for solving quadratic equations, simplifying complex expressions, and exploring mathematical relationships in various fields of study.