Collecting like terms
Match all pronumeral factors and powers. Add signed coefficients and retain separate unlike groups
\[7x-11x=-4x\]
- Match factors and powers Two terms are like when their pronumeral factors and powers are identical. Coefficients may differ
- Order does not matter Multiplication can be reordered, so ab and ba have the same pronumeral part \(\displaystyle ab=ba\)
- Keep the sign Add the signed coefficients; keep the pronumeral part unchanged \(\displaystyle 6x-9x=-3x\)
- Keep unlike terms separate The terms x and x squared cannot be collected. They may happen to have equal values for a particular x; that does not make them like terms
- Cancellation and constants A zero coefficient removes that group. All constant terms can be collected \(\displaystyle 4x-4x+7-2=5\)
Worked example
Collect each type of term, then combine the results
\[8a^{2}-3a+5a^{2}+2a-4\]
- \(\displaystyle 8a^{2}+5a^{2}=13a^{2}\)Collect the squared terms
- \(\displaystyle -3a+2a=-a\)Add the signed linear coefficients
- \(\displaystyle 13a^{2}-a-4\)Keep the constant, squared and linear terms separate
Common mistakes
Matching only a letter
✕\(\displaystyle 4x+3x^{2}=7x^{2}\)✓\(\displaystyle 3x^{2}+4x\)
Different powers remain separateLosing a negative sign
✕\(\displaystyle 6a-9a=15a\)✓\(\displaystyle 6a-9a=-3a\)
Add six and negative nineSubtracting only the first term
✕\(\displaystyle -(2x+5)=-2x+5\)✓\(\displaystyle -(2x+5)=-2x-5\)
A minus before a group applies to every termDifficulty levels
introCollect positive coefficients in two like-term groups
standardIdentify like-term groups among signed terms and different powers
challengeIdentify and collect groups with negative totals or cancellation
examChoose the simplified expression using factors, powers and signs
Questions about this topic
Are ab and ba like terms?+
Yes. Multiplication can be reordered, so their pronumeral parts are identical
Can a squared term and a linear term be collected?+
No. Their powers differ, even if they have equal numerical values at a particular substitution
What happens when a coefficient total is zero?+
That whole like-term group contributes zero and can be omitted
Can constants be collected?+
Yes. Add their signed values
How do I subtract an expression?+
Change every sign in the expression being subtracted, then collect matching terms
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 3: Algebra and indices
In this chapter
Identify the parts of an algebraic expressionForm and evaluate algebraic expressionsSubstitute values into a formulaEvaluate an integer expressionIdentify and collect like termsMultiply and divide algebraic termsExpand brackets and simplifyFind the HCF and factorise algebraic expressionsSimplify, multiply and divide algebraic fractionsAdd and subtract algebraic fractionsIndex notation and index laws 1 and 2Index laws 3 to 5 and the zero powerNegative indices and combined index lawsScientific notationRound to decimal places or significant figuresScientific notation with significant figuresExponential growth, decay and compound interestModel a compound-interest investment or loan with a recurrence relationFind term n of a geometric sequence using the ruleInterpret and use logarithmic scalesImplement algorithms with lists