Algebraic Expressions — REET Maths Notes
Algebraic expressions are built by combining variables and constants through addition, subtraction and multiplication, and they form the foundation of the Algebra section of the REET maths paper. This page explains terms, coefficients, degree, like and unlike terms, and the different types of expressions with worked examples, so that later topics like factorisation and equations become easier to grasp.
- 0 questions in REET 2024
- Class 7 level
- 9 min read
How this topic is asked in REET
The Algebra section of the REET maths syllabus includes basic building blocks like algebraic expressions. No direct question from this specific sub-topic showed up in the REET 2024 paper, so this page is built on standard syllabus facts and the NCERT Class 7 maths textbook. Typically, questions ask you to identify a term, coefficient or degree of an expression, or to add or subtract two expressions. Occasionally you're asked to classify an expression as a monomial/binomial/trinomial, or to evaluate an expression after substituting a given value for the variable.
What is an algebraic expression
When variables (like x, y) and constants (like 2, −5) are combined through addition, subtraction, multiplication or division, the resulting quantity is called an algebraic expression — for example, 5x + 3y − 7. Each part of the expression that is separated by a + or − sign is called a term.
Algebra takes ordinary arithmetic a step further by letting you work with unknown quantities. While arithmetic works only with fixed numbers (like 5 + 3), algebra uses symbols such as x and y to write general rules and formulas that stay true for every possible value — and this generality is exactly what makes algebraic expressions so useful.
Algebraic expressions go on to form the base for several important topics — factorisation, identities and linear equations. So only once basics like terms, coefficients and like/unlike terms are absolutely clear does the more advanced material become easy to follow — that's exactly why this topic is recommended as one of the first stops in REET maths preparation.
Basic vocabulary of an expression
| Term | Meaning | Example (3x² − 5xy + 7) |
|---|---|---|
| Variable | A quantity whose value can change | x, y |
| Constant | A quantity with a fixed value | 7 |
| Term | A part of the expression separated by a + or − sign | 3x², −5xy, 7 |
| Coefficient | The number multiplied with the variable in a term | In 3x² the coefficient is 3; in −5xy the coefficient is −5 |
| Degree | The sum of the powers of the variables in a term; the highest such sum in the expression | 3x² has degree 2; −5xy has degree 2 (1+1); so the expression has degree 2 |
Types of expressions, by number of terms
| Type | Definition | Example |
|---|---|---|
| Monomial | An expression with only one term | 5x, −3ab, 7 |
| Binomial | An expression with two unlike terms | 2a + 3b, x² − 5 |
| Trinomial | An expression with three unlike terms | a + 2b + 5c |
| Polynomial | The general term for an expression with one or more terms | x³ + 2x² − x + 1 |
In its broader sense, 'polynomial' also covers monomials, binomials and trinomials
Like and unlike terms
- Like terms
- Terms in which the variables and their powers are identical — only the coefficient can differ, e.g. 5x and −3x
- Unlike terms
- Terms in which the variables or their powers differ, e.g. 5x and 4x²y
- Rule for adding and subtracting
- Only like terms can be directly added or subtracted; unlike terms stay unchanged within the expression
- Quick way to spot them
- Two terms count as like terms only when all their variables and every variable's power match exactly — the coefficient can be anything
Evaluating an expression
Evaluating an algebraic expression means finding its value after substituting a given numerical value in place of the variable. Example: if x = 2 and y = 3, then the value of the expression 3x² − 5xy + 2y² − 7 is 3(2)² − 5(2)(3) + 2(3)² − 7 = 12 − 30 + 18 − 7 = −7. When evaluating, solve powers first, then multiplication, and finally addition and subtraction — this is simply the correct order of operations (BODMAS).
A common mistake during evaluation is forgetting to bracket a negative value, which leads to a sign error — for example, when substituting x = −2, you should write 3x² as 3(−2)², not as 3−2², because the two give completely different results. So always place a negative value inside brackets before substituting it into the expression.
How to teach this to children
Classroom activity
Use groups of matchsticks or marbles to introduce the feel of a variable through language like 'x number of matchsticks', then have students combine two separate groups to build an expression and verify it by substituting different values of x.
Teaching aid
Write terms on differently coloured cards (say 3x on green, 5y on blue) and have students practise combining only same-colour (like) terms, while keeping different-coloured (unlike) ones apart.
Common misconception
Students often treat 5x and 5x² as like terms, when in fact the different powers make them unlike terms that cannot be directly combined — clear this up with a substituted example, showing the two give different values.
Assessment idea
Give students a mixed list of 8–10 terms and have them sort these into groups of like terms and combine each group, then give a value for the variable and have them evaluate the whole expression as well.
A trick worth remembering
Before adding or subtracting, do a 'variable check' — only combine two terms when their variables and powers are exactly the same; otherwise, leave them written separately. To avoid mistakes while subtracting, flip the sign of every term in the expression being subtracted first, then combine like terms — this approach cuts down on errors considerably.
Practice questions
Question 1
The number of terms in the expression 5x + 3y − 2 is—
- A2
- B3
- C4
- D1
Explanation
This expression has three terms — 5x, 3y and −2.
Question 2
In the expression 7ab, the coefficient is—
- Aa
- Bb
- C7
- Dab
Explanation
In the term 7ab, the number multiplied with the variable 'ab' is 7, which is the coefficient.
Question 3
Which of the following is a monomial?
- A5x + 3
- Bx² − y²
- C7xy
- Da + b + c
Explanation
'7xy' has only one term, so it is a monomial; every other option has two or more terms.
Question 4
What type of terms are 5x² and −3x²?
- Aअसमान पद
- Bसमान पद
- Cअचर पद
- Dइनमें से कोई नहीं
Explanation
Both terms share the same variable 'x' and the same power '2' — only the coefficient differs — so these are like terms.
Question 5
The degree of the expression 3x² − 5xy + 2y² − 7 is—
- A1
- B2
- C3
- D4
Explanation
Sum of powers in each term: 3x² has degree 2, −5xy has degree 1+1=2, 2y² has degree 2, and −7 has degree 0; the largest degree present is 2, so the expression's degree is 2.
Question 6
Adding (5x + 3y) and (2x − y) gives the expression—
- A7x + 2y
- B3x + 4y
- C7x + 4y
- D3x + 2y
Explanation
Combine like terms: 5x + 2x = 7x and 3y + (−y) = 2y, so the sum is 7x + 2y.
Question 7
Subtracting (3a − 2b) from (7a − 4b) gives the expression—
- A4a − 2b
- B4a − 6b
- C10a − 6b
- D4a + 2b
Explanation
(7a − 4b) − (3a − 2b) = 7a − 4b − 3a + 2b = 4a − 2b.
Question 8
An expression has three unlike terms, 2x, −3y and 5. What is this expression called?
- Aएकपदी
- Bद्विपदी
- Cत्रिपदी
- Dसमान पदों का व्यंजक
Explanation
An expression with three unlike terms is called a trinomial.
Question 9
The degree of x²y is—
- A1
- B2
- C3
- D0
Explanation
Degree = power of x (2) + power of y (1) = 3.
Question 10
Class 7 students mistakenly believe that 5x and 5x² are like terms. What is the best step a teacher can take to clear this misconception?
- Aविद्यार्थियों को बताएँ कि समान पद के लिए चर के साथ-साथ घात भी समान होनी चाहिए, और x=2 रखकर x तथा x² के अलग-अलग मान (2 और 4) दिखाकर अंतर स्पष्ट करें
- Bविषय पर आगे चर्चा न करें
- Cकेवल परिभाषा दोहराएँ
- Dविद्यार्थियों को बिना स्पष्टीकरण गलत बताकर आगे बढ़ें
Explanation
Showing a substituted example — where x=2 gives x the value 2 and x² the value 4 — makes it concrete that a different power means the terms are unlike, even though they share the same variable letter.
Frequently asked questions
How are algebraic expressions asked about in REET?+
Usually as simple computational questions — identifying a term, coefficient or degree of an expression, or adding and subtracting two expressions.
What's the difference between a monomial and a binomial?+
A monomial has only one term (like 5x), while a binomial has two unlike terms joined by addition or subtraction (like 2a + 3b).
How do you identify like terms?+
Terms whose variables and powers are exactly the same, with only the coefficient allowed to differ, are called like terms — for example, 4x² and −7x².
How do you find the degree of an expression?+
Add up the powers of the variables present in each term, and the largest such sum across all terms is the degree of the expression.
What does 'evaluating' an expression mean?+
Finding the value of an expression after substituting a fixed numerical value for the variable is called evaluation — for example, substituting x = 2 gives 3x + 1 the value 3(2) + 1 = 7.
Read next
Cubes and Cube Roots
Cubes and cube roots — the previous topic in the REET maths sequence
Factorisation
Factorising expressions — the next topic in the REET maths sequence
REET Syllabus
The complete official syllabus for REET Level 1 and Level 2, in one place
REET 2024 Solved Paper
All solved REET 2024 questions, organised subject-wise
Change Log
- 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked