⭐ Answer Key included!
Worksheet on factorisation techniques for Class 8 with 24 problems. Learn common factor method, difference of squares, perfect square trinomials, splitting middle term, and regrouping with detailed solutions.
Factorisation is the process of expressing an algebraic expression as a product of its factors. It is the reverse process of expanding brackets.
Common Factor Method: ab + ac = a(b + c)
Difference of Squares: a² - b² = (a + b)(a - b)
Perfect Square Trinomial:
Splitting the Middle Term: For x² + bx + c, find two numbers whose product = c and sum = b
Regrouping Method: Group terms to find common factors
Simplifies algebraic expressions
Helps solve equations
Used in finding HCF and LCM of algebraic expressions
Essential for higher mathematics like calculus
Problem: Factorise x² - 16
Solution:
Step 1: Recognize that x² - 16 is a difference of two squares
Step 2: Write each term as a square: x² = (x)² and 16 = (4)²
Step 3: Apply the identity: a² - b² = (a + b)(a - b)
Step 4: Substitute: x² - 16 = (x)² - (4)² = (x + 4)(x - 4)
Verification: (x + 4)(x - 4) = x² - 4x + 4x - 16 = x² - 16 ✓
Factorise: 6x + 9
Find the common factor and factorise: 12a²b + 8ab²
Factorise using the identity a² - b²: y² - 25
Factorise the perfect square: p² + 6p + 9
Factorise by splitting the middle term: x² + 7x + 12
Factorise by regrouping: 2ax + bx + 2ay + by
Factorise: 4x² - 12xy + 9y²
Word Problem: The area of a rectangular garden is given by (x² + 8x + 15) square meters. If the length is (x + 5) meters, find the width by factorising the area.
Factorise: a² - 2ab + b² - c²
Factorise completely: 3x² - 27
Factorise: x⁴ - 81
Factorise by regrouping: xy² - xz² + y² - z²
Application Problem: The difference between the squares of two consecutive odd numbers is always divisible by 8. Prove this algebraically by taking two consecutive odd numbers as (2n + 1) and (2n + 3), and factorising (2n + 3)² - (2n + 1)².
20-24 correct: Excellent! Outstanding! Move on to algebraic identities applications, simultaneous equations, and polynomial division.
15-19 correct: Very Good! Great work! Practice more regrouping problems and complex identities. Focus on word problems involving factorisation.
10-14 correct: Good Effort! Keep practicing! Focus on memorizing the key identities and practice splitting the middle term. Work on 10-15 more problems daily.
0-9 correct: Keep Trying! Review the concept section carefully. Start with common factor method, then move to difference of squares. Practice basic identities daily.
Memorize key identities: Write (a+b)², (a-b)², and a²-b² on flashcards
Look for patterns: Always check for common factors first
Practice splitting: For x² + bx + c, find two numbers that multiply to c and add to b
Verify your answer: Expand your factorised form to check if it matches the original
Group intelligently: In regrouping method, try different groupings if first attempt doesn't work
Work systematically: Follow these steps - Common factor → Identities → Splitting → Regrouping
Forgetting to take out common factors before applying identities
Confusing (a+b)² with a² + b² (remember the 2ab term!)
Trying to factorise x² + k² (sum of squares doesn't factorise with real numbers)
Wrong signs when splitting the middle term
Not factorising completely (always check if factors can be factorised further)
Forgetting to apply distributive property when verifying
Class 8 Algebraic Expressions
Class 8 Direct and Inverse Proportion
Class 8 Exponents and Powers
Class 8 Factorisation
Class 8 Mensuration
Class 8 Rational Numbers
Not in Class 8?
Visit our Main Math Worksheet Hub to explore all printable worksheets from Class 2 to Class 8.
