About this video
How to factorise an expression with four terms by grouping them in pairs — an essential technique for Grade 10 algebra.
What it covers
- Spotting when to group: four terms
- Taking out a common factor from each pair
- Taking out a negative when the brackets have opposite signs
- Rearranging the terms so each pair has a common factor
- Taking out the common bracket
Extra worked examples
✍️ Extra example: factorise 6ax − 6ay − 5x + 5y
- 16a(x − y) − 5x + 5yCommon factor of the first pair.
- 26a(x − y) − 5(x − y)Take out −5 so the signs inside match: −5x + 5y = −5(x − y).
- 3(x − y)(6a − 5)Take out the common bracket.
✍️ Extra example: factorise ab + 2c + 2b + ac
- 1ab + 2b + 2c + acThe first two terms share nothing — rearrange so each pair has a common factor.
- 2b(a + 2) + c(2 + a)2 + a is the same bracket as a + 2.
- 3(a + 2)(b + c)Take out the common bracket. Grouping a different way gives the same answer.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Factorise xy + 4x + 3y + 12.
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x(y + 4) + 3(y + 4) = (y + 4)(x + 3) - 2Factorise 2ab − 6a + b − 3.
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2a(b − 3) + 1(b − 3) = (b − 3)(2a + 1) - 3Factorise pq − p − 2q + 2.
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p(q − 1) − 2(q − 1) = (q − 1)(p − 2) - 4Factorise 3x + xy + 3z + yz.
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x(3 + y) + z(3 + y) = (3 + y)(x + z) - 5Factorise m² − mn + 4m − 4n.
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m(m − n) + 4(m − n) = (m − n)(m + 4)
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