Factorising by Grouping Flashcards

All 4 cards in this deck

What is factorising by grouping, and when is it used?

Used for four terms with no single common factor: pair the terms, take a common factor out of each pair, then take out the identical bracket.

What are the steps to factorise four terms by grouping?

e.g. $ax + bx - ay - by$

1. Pair the terms: $(ax + bx) + (-ay - by)$
2. Factorise each pair: $x(a + b) - y(a + b)$
3. Take out the common bracket: $(a + b)(x - y)$

True or false? When grouping, if the two brackets after factorising each pair are not identical, you cannot finish the factorisation that way.

True. You must re-pair the terms or take out a negative factor so the brackets match.

When grouping, what do you take out of a pair whose first term is negative?

e.g. $-ay - by$

A negative common factor, so the bracket comes out positive.

Here: $-y(a + b)$