Algebra (Classes VI-VIII) • Topic 1 of 4

Algebraic Expressions

An algebraic expression is built from variables (letters like x, y that stand for unknown or changing numbers), constants (fixed numbers) and operations. CTET expects you to read an expression the way a child should: 5x + 3 is a term 5x added to a constant 3, where 5 is the coefficient of x. The single most tested idea here is like terms -- terms with exactly the same variable part can be combined, terms with different variable parts cannot. A child who writes 3 + 2x = 5x has fallen into the classic 'conjoining' error: treating the plus sign as a command to finish the sum and gluing unlike things together. Another child reads 2x as 'two-then-x' rather than '2 times x'. Good teaching here is concrete first -- using matchsticks or tiles so the variable feels like a real, countable quantity before the symbol takes over -- and CTET rewards the answer that keeps the letter meaningful (x as a number) rather than treating it as a label for an object ('a for apples'), which is a well-known misconception trap the exam plants deliberately. Watch the difference between an expression (no equals sign, cannot be 'solved', only simplified or evaluated) and an equation.

✅ Solved examples

1. A child simplifies 3 + 2x and writes the answer as 5x. What is the error, and what is the correct simplified form?
The child has joined unlike terms (the 'conjoining' or detached-symbol error): 3 is a constant and 2x has a variable, so they are not like terms and cannot be added into one term. The expression 3 + 2x is already in simplest form.
2. In the term 7xy, identify the coefficient of xy and the variables.
The coefficient is 7; the variables are x and y. The term means 7 times x times y.
3. Simplify 6a + 2b - 4a + 5b.
Group like terms: (6a - 4a) + (2b + 5b) = 2a + 7b. Only terms with the same variable part are combined.
4. A teacher tells students 'in 4a, a stands for apple'. Why is this a poor pedagogical choice?
It teaches the variable as a label for an object rather than as a number. The fruit-salad idea breaks down the moment children must evaluate (a = 3) or multiply, so CTET treats the 'letter as object' analogy as a misconception to avoid.

✏️ Practice — try these, take hints as needed

1. Simplify: 9m - 3 + 2m + 7.
Collect the m terms together.
Collect the constants together.
You should get one variable term and one constant.
11m + 4
2. How many terms are there in the expression 5x^2 - 3x + 8, and what is the constant term?
Terms are separated by + or - signs.
The constant has no variable.
3 terms; constant term is 8
3. Are 4xy and 4yx like terms or unlike terms?
Multiplication does not care about order.
Compare the variable parts.
Like terms (xy = yx), so they can be combined
4. Why can 3 + 2x NOT be written as 5x?
Look at whether the two terms share the same variable part.
One is a constant.
Because 3 and 2x are unlike terms (a constant and a variable term) and cannot be added into one term

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
Linear Equations in One Variable →