Factorisation by Grouping Worksheet

Factorisation by Grouping

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 \( 3x^3 + 5x^2 - 12x - 20 \)?

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: \( a^2 + b^2 - c^2 - d^2 + 2ab + 2cd \)