Factorisation by Grouping Worksheet
Grade 12 Math worksheet focusing on factorisation by grouping, including advanced algebraic expressions and problem-solving.
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Factorisation by Grouping
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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: \( a^2 + b^2 - c^2 - d^2 + 2ab + 2cd \)