Factorisation by Grouping Worksheet
Grade 10 Math worksheet on factorisation by grouping with various question types.
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Factorisation by Grouping
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Read each question carefully and factorise the given expressions by grouping. Show all your steps.
1. Factorise the expression: ax + ay + bx + by
2. Factorise the expression: x³ + 2x² + 5x + 10
3. Factorise the expression: 2xy - 4x + 3y - 6
1. To factorise 3x² + 6x + 4x + 8 by grouping, the first step is to group the terms: (3x² + 6x) + (4x + 8). Then, factor out the common factor from each group: 3x(x + 2) + 4(x + 2). Finally, factor out the common binomial factor: .
2. When factorising 5y² - 10y + 7y - 14, the common factor for the first group (5y² - 10y) is 5y, resulting in 5y(y - 2). The common factor for the second group (7y - 14) is , which gives 7(y - 2). The final factorised form is (5y + 7)(y - 2).
1. Which of the following is the correct factorisation of 6ab - 9a + 2b - 3?
(3a + 1)(2b - 3)
(3a - 1)(2b + 3)
(3a + 1)(2b + 3)
(3a - 1)(2b - 3)
2. What is the common binomial factor when factorising x² + 3x + 4x + 12?
(x + 3)
(x + 4)
(x²)
(3x)
1. Factorisation by grouping is only applicable to expressions with four terms.
True
False
2. The expression x² - 5x + 2x - 10 can be factorised as (x - 5)(x + 2).
True
False
Factorise the expression: a³ - a²b + ab² - b³
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