Factorising by grouping

Factorising by Grouping

Introduction

• Factorising by grouping is a handy tool to deconstruct algebraic expressions into simpler factors.
• The process involves grouping terms that share common factors and factorising them out.

The Process of Factorising by Grouping

• In a four term expression, create two groups, each consisting of two terms.
• For each group, factor out the Greatest Common Factor (GCF). This results in two terms, each of which should now share a common binomial.
• Factor out this common binomial. Your expression is now decomposed into the product of two binomials.

Factorising by Grouping in Practice

• When presented with four-term expressions, factorising by grouping simplifies the expression.
• The choice of grouping, whilst typically evident, may need reworking if a common binomial does not emerge.
• If there is no common factor, try reordering the terms and then regroup. Sometimes a different arrangement can reveal a common factor.

Examples

• For example, with the expression 3ax + 3ay + 2bx + 2by, divide it into two groups (3ax + 3ay) and (2bx + 2by). Factorise these to give 3a(x + y) + 2b(x + y). Now, x + y is the common factor, thus it becomes (3a + 2b)(x + y).
• As another example, for ab + ac + db + dc, the groups could be (ab + ac) and (db + dc). This gives a(b + c) + d(b + c), which simplifies to (a + d)(b + c).

Conclusion

• Practice is essential to becoming proficient in factorising by grouping. With proper understanding and frequent repetition, it becomes easier to spot patterns and determine how to group terms effectively.
• Becoming proficient in factorising by grouping sets a foundation for tackling more complex algebraic manipulations. It’s a powerful tool, helping to simplify expressions and solve equations more seasoned and efficiently.