Factorisation by Grouping Worksheet
Grade 12 Math worksheet focusing on factorisation by grouping, including advanced algebraic expressions and problem-solving.
Includes
Standards
Topics
Factorisation by Grouping
Name:
Date:
Score:
Carefully read each question and factorise the given algebraic expressions by grouping terms. Show all your steps clearly. Simplify your final answers.
1. Factorise the expression: \( ax + ay + bx + by \)
2. Factorise the expression: \( 2x^2 + 6xy - 3x - 9y \)
3. Factorise the expression completely: \( x^3 - 2x^2 - 9x + 18 \)
4. Factorise: \( 4a^2 - 2ab - 6ac + 3bc \)
5. Which of the following is a factor of \( 3x^3 + 5x^2 - 12x - 20 \)?
\( (x+2) \)
\( (3x-5) \)
\( (x-2) \)
\( (3x+4) \)
6. When factorising \( x^2y - x^2z + xy^2 - xyz \) by grouping, one of the common factors after the first step is .
7. The completely factorised form of \( 6p^2 + 15pq - 4pr - 10qr \) is .
8. Factorise the following expression, which requires rearranging terms before grouping: \( a^2 + b^2 - c^2 - d^2 + 2ab + 2cd \)
Related Worksheets
Perfect Square Trinomials
This worksheet focuses on identifying, factoring, and constructing perfect square trinomials, essential skills for Grade 12 Algebra.
Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
Grade 12 Algebra: Standard Form
A Grade 12 math worksheet focusing on converting between different forms of linear equations, identifying slopes and intercepts, and graphing linear equations in standard form.
Characteristics of Parabolas Worksheet
Explore and identify the key characteristics of parabolas, including vertex, focus, directrix, and axis of symmetry.
Solving Equations with Variables on Both Sides
This worksheet provides practice on solving linear equations where variables appear on both sides of the equals sign.
Evaluating Algebraic Expressions
This worksheet focuses on evaluating complex algebraic expressions involving various operations and functions, suitable for Grade 12 students.
Graphing Parabolas Worksheet
A Grade 12 math worksheet on graphing parabolas, covering standard form, vertex form, and intercepts.
Grade 12 Sigma Notation Worksheet
A comprehensive worksheet for Grade 12 students covering sigma notation, including evaluating sums, expanding series, and writing expressions in sigma notation.