Mathematics (Core)Exam code: 0580
Expanding and Factorising Brackets
Algebra and Sequences
Reversing the expansion
- Factorising writes an expression as a product, which is the reverse of expanding
- Take the largest number dividing every coefficient, together with the highest power of each letter that divides every term
- Dividing each term by that combined factor leaves what belongs inside the bracket
- 20p³ − 15p² has highest common factor 5p², giving 5p²(4p − 3)
- Expanding the answer back is a reliable check, and it costs one line
Exam tip
Take out every common factor
Set in 11 of the 22 papers. Taking out only the number, as in 4(3x² − 2x), or only the letter, as in x(12x − 8), earns one of the two marks; the second needs both, 4x(3x − 2). Expanding back cannot catch this, because a partial answer expands correctly too, so check that the terms left in the bracket share no factor at all.
Worked example
Taking out a common factor
Factorise 12x³ − 18x².
Solution:
- Find the highest common factor of the numbers and of the letters separately
- The highest common factor of 12 and 18 is 6
- Both terms contain x², and that is the highest power common to both
- So the common factor is 6x²
- 12x³ ÷ 6x² = 2x, and −18x² ÷ 6x² = −3
- 12x³ − 18x² = 6x²(2x − 3)
- Check by expanding back