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Identify the parts of an algebraic expression

Start a set of 8
Step 3 of 11

Read terms, factors and coefficients

These examples are expanded expressions. Count signed terms, not the factors or tiles inside a term

  1. 1Keep the sign In an expanded expression, separate terms at addition and subtraction signs. Keep each sign with its term \(\displaystyle -3x^2+5x-7\)
  2. 2A product stays together The factors in a product form one term. A plus sign inside brackets does not split an outer product \(\displaystyle 4xy=4\times x\times y\)
  3. 3Invisible ones A pronumeral written without a number has numerical coefficient one or negative one \(\displaystyle -x=(-1)\times x\)
  4. 4Constants and zero terms A constant has no pronumeral. If none is written, the constant term is zero. A zero-coefficient term vanishes \(\displaystyle 0x=0\)
Year 10, Chapter 3, 4 difficulty levels, No calculatorBuild a worksheet

Expression structure

A numerical coefficient is the signed number multiplying a specified pronumeral part. State exactly which term is meant when products and single pronumerals both occur

  1. Keep the sign In an expanded expression, separate terms at addition and subtraction signs. Keep each sign with its term \(\displaystyle -3x^2+5x-7\)
  2. A product stays together The factors in a product form one term. A plus sign inside brackets does not split an outer product \(\displaystyle 4xy=4\times x\times y\)
  3. Invisible ones A pronumeral written without a number has numerical coefficient one or negative one \(\displaystyle -x=(-1)\times x\)
  4. Constants and zero terms A constant has no pronumeral. If none is written, the constant term is zero. A zero-coefficient term vanishes \(\displaystyle 0x=0\)

Worked example

Identify the terms and numerical coefficients in this expanded expression

\[5a^2-3ab+a-8\]
  1. \(\displaystyle 5a^2,\quad-3ab,\quad a,\quad-8\)There are four signed terms; the constant is negative eight
  2. \(\displaystyle 5a^2=5\times a^2\)The squared term has numerical coefficient five
  3. \(\displaystyle -3ab=(-3)\times ab\)The product term has numerical coefficient negative three
  4. \(\displaystyle a=1\times a\)The standalone a term has numerical coefficient one

Common mistakes

Counting factors as terms
✕\(\displaystyle 4xy:\;3\text{ terms}\)✓\(\displaystyle 4xy:\;1\text{ term}\)
The number and pronumerals are multiplied within one term
Dropping the sign
✕\(\displaystyle -x=1\times x\)✓\(\displaystyle -x=(-1)\times x\)
The negative sign belongs to the numerical coefficient
Confusing a coefficient with a constant
✕\(\displaystyle -4x^2+9:\;c=-4\)✓\(\displaystyle -4x^2+9:\;c=9\)
Here c denotes the constant term. Negative four multiplies the squared term; nine has no pronumeral

Difficulty levels

introIdentify the parts of short positive expressions
standardSelect signed coefficients and constant terms
challengeRead products, powers and implicit unit coefficients
examDistinguish coefficients from exponents, constants and term counts

Questions about this topic

Why can a coefficient be negative?+

It includes the sign of its term. Negative three x is negative three multiplied by x.

Do several tiles mean several terms?+

No. Tiles of the same pronumeral part represent one term with a larger coefficient

What if a constant is missing?+

The constant term is zero. A term with zero coefficient contributes nothing and can be omitted

Can I split at a sign inside brackets?+

First identify the outer operations. A bracket multiplied by another factor is a single outer term until expanded

Why specify the standalone term?+

An expression can contain both l and wl. Asking for the numerical coefficient of the standalone l term avoids confusing it with the product term

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