Definition
Factorise an expression
Factorise an expression by rewriting a sum or difference as an equivalent product of factors.
What it means
Factorising packs terms into brackets. Find a factor that every term shares, place it outside, and write what remains inside. Expand your result to check it: if you get the starting expression back, the factorisation is correct.
Remember it
Find what every term shares, then pack the leftovers inside brackets.
Example
Factorise 15x + 20. Both terms share a factor of 5. Divide each term by 5 to get 3x and 4, so 15x + 20 = 5(3x + 4). Expanding checks the result.
Watch for
A factor outside the brackets must divide every original term. The form 5(3x + 20) is not equal to 15x + 20 because it expands to 15x + 100.
Common mix-up
Factorising packs a sum or difference into a product. Expanding opens a product into a sum or difference.
Exact meaning
Factorising an expression rewrites it as an equivalent product. In elementary algebra, this usually means taking out a factor shared by every term so that expanding the product returns the original expression.