CBSE Class 7 Maths — Algebraic Expressions

Chapter Overview & Weightage

Algebraic Expressions in Class 7 is one of the most important chapters — it builds the foundation for all algebra in Class 8, 9, 10, and beyond. Students who struggle with algebraic manipulation in Class 9 often trace the problem back to shaky foundations from this chapter.

In CBSE Class 7 exams, this chapter typically carries:

Exam Component	Marks
Very Short Answer (1 mark each)	2–3 marks
Short Answer (2–3 marks each)	6–8 marks
Long Answer (4–5 marks)	4–5 marks
Total	~15 marks

This chapter has steady marks every year. Addition/subtraction of expressions, finding values by substitution, and identifying “like terms” are the most frequently tested skills.

Key Concepts You Must Know

Variable: A letter that represents an unknown or changing quantity. Example: $x$ , $y$ , $a$ .

Constant: A fixed numerical value. Example: 3, −5, $\pi$ .

Algebraic expression: A combination of variables and constants connected by operations (+, −, ×, ÷). Example: $3x + 5y - 2$ .

Term: Each part of an expression separated by + or −. Example: in $3x + 5y - 2$ , the terms are $3x$ , $5y$ , and $-2$ .

Coefficient: The numerical part of a term. In $3x$ , the coefficient of $x$ is 3. In $-5y^2$ , the coefficient of $y^2$ is $-5$ .

Like terms: Terms with the same variable(s) raised to the same power. Example: $3x$ and $-7x$ are like terms; $3x$ and $3x^2$ are NOT.

Unlike terms: Terms with different variables or different powers.

Monomial: Expression with exactly one term (e.g., $5x^2$ ). Binomial: Two terms (e.g., $3x + 4$ ). Trinomial: Three terms (e.g., $x^2 + 2x + 1$ ). Polynomial: One or more terms.

Important Formulas

Rule: Only like terms can be added or subtracted. Collect like terms together, then add/subtract their coefficients.

Example: $(3x + 5y) + (2x - 3y)$ = $(3x + 2x) + (5y - 3y)$ = $5x + 2y$

For subtraction, change the sign of every term in the expression being subtracted, then add.

$(5x + 3) - (2x - 7) = 5x + 3 - 2x + 7 = 3x + 10$

Replace every variable with its given numerical value, then compute.

Example: Find $3x^2 - 2x + 5$ when $x = 2$ : $= 3(2)^2 - 2(2) + 5 = 3(4) - 4 + 5 = 12 - 4 + 5 = 13$

Solved Previous Year Questions

PYQ 1 — Like and Unlike Terms (CBSE SA1 type)

Q: Identify like terms in: $3x$ , $4y$ , $-5x$ , $2xy$ , $7y$ , $-3xy$ .

Solution:

Like terms share the same variable:

Like terms with $x$ : $3x$ and $-5x$
Like terms with $y$ : $4y$ and $7y$
Like terms with $xy$ : $2xy$ and $-3xy$

Simplified: $-2x + 11y - xy$ .

PYQ 2 — Addition of Expressions (SA1)

Q: Add $3x^2 + 5x - 4$ and $-2x^2 - 3x + 7$ .

Solution:

Arrange like terms in columns:

  3x² + 5x - 4
+ (-2x² - 3x + 7)
─────────────────
  x²  + 2x + 3

Answer: $x^2 + 2x + 3$

PYQ 3 — Subtraction (SA2 type)

Q: Subtract $2a + 3b - 4c$ from $5a - 2b + 6c$ .

Solution:

“Subtract A from B” means “B − A.” So:

$(5a - 2b + 6c) - (2a + 3b - 4c)$

Change signs of second expression: $= 5a - 2b + 6c - 2a - 3b + 4c$

Collect like terms: $= (5a - 2a) + (-2b - 3b) + (6c + 4c) = 3a - 5b + 10c$

PYQ 4 — Value of Expression (2–3 mark)

Q: Find the value of $4p^2 - 3p + 5$ when $p = -2$ .

Solution:

$= 4(-2)^2 - 3(-2) + 5$ $= 4(4) + 6 + 5$ $= 16 + 6 + 5 = 27$

Watch the sign: $(-2)^2 = +4$ and $-3 \times (-2) = +6$ .

Difficulty Distribution

Level	Percentage	Question Types
Easy	40%	Identify terms/coefficients, simple addition of monomials
Medium	45%	Subtract expressions, find value by substitution
Hard	15%	Multi-step problems, forming expressions from word problems

The “hard” questions in this chapter are almost always word problems: “The length of a rectangle is $2x + 3$ and width is $x - 1$ . Find the perimeter.” The maths is straightforward — the challenge is translating words into algebra. Practice 5–10 word problems before the exam.

Expert Strategy

Step 1: Make sure you can instantly recognise like terms. Write a set of 10 terms and practice grouping them in 30 seconds.

Step 2: For subtraction, ALWAYS change the sign of every term in the bracket being subtracted, then add. Write this as an explicit step — students who do it in their head make sign errors.

Step 3: For substitution, substitute the value with brackets around it — especially for negative numbers. Write $(-2)$ not just $-2$ when substituting.

In the exam: Show all steps. Even if you can do simple addition mentally, write the “collecting like terms” step. Examiners award process marks.

CBSE Class 7 exams often ask students to “add” or “subtract” two expressions — the answer must be in simplest form (like terms collected). An unsimplified answer like " $3x + 2x + 4y$ " will lose half marks even if no arithmetic was wrong. Always simplify to ” $5x + 4y$ .”

Common Traps

Trap 1: Sign errors in subtraction. When subtracting $(2x - 5)$ , every term changes sign: it becomes $-2x + 5$ . Students often change only the first sign and write $-2x - 5$ . Bracket and sign it explicitly every time.

Trap 2: Treating $3x$ and $3x^2$ as like terms. They are NOT — the powers are different. Only combine terms with identical variable-power combinations.

Trap 3: Adding coefficients when no operation is shown. $3x \times 4x = 12x^2$ (multiply both coefficients AND add exponents). $3x + 4x = 7x$ (only add coefficients). Mixing these rules is extremely common.

Trap 4: Forgetting that a term can be a constant (number without any variable). In $3x + 5y - 7$ , the constant term is $-7$ . It can only be combined with other constants.