Algebraic Expressions — Class 7 IMO

Terms, Coefficients & Like Terms

Like terms have the same variable raised to the same power. Constants (plain numbers) are also like terms with each other.

Expression	Like Terms	Unlike Terms
4x + 2x	4x and 2x (same variable)	—
3x + 2y	—	3x and 2y (different variables)
5x^2 + 3x	—	5x^2 and 3x (different powers)

Rules for combining like terms:

Add or subtract the coefficients only
The variable part stays unchanged
Always carry the sign (+ or -) with each term

LIKE TERMS SORTING:

Expression: 4x + 2y - x + 3y

Step 1: Group like terms
  x-terms: 4x and -x
  y-terms: 2y and 3y

Step 2: Combine
  (4x - x) = 3x
  (2y + 3y) = 5y

Final Answer: 3x + 5y

Example 1: In the term 5x, what is the coefficient?

5.

Example 2: Are 3x and 7x like or unlike terms?

Like terms — same variable part x.

Example 3: Simplify: 7a + 3b - 2a + 4b

Group like terms: (7a - 2a) + (3b + 4b) = 5a + 7b

Example 4: Simplify: 5x + 2 - 3x + 7

Group like terms: (5x - 3x) + (2 + 7) = 2x + 9

Example 5: Simplify: 4m - 2n + 3m + n - 5

(4m + 3m) + (-2n + n) - 5 = 7m - n - 5

Quick recap

Coefficient = the number multiplying the variable.
Like terms have the same variable part.
Only like terms (same variable AND same exponent) can be combined
Add or subtract only the coefficients
The variable part does not change when combining
Always carry the sign with each term

✓ Quick check

What is the coefficient of x in 8x?

The number multiplying x is 8.

Which are like terms?

2x and 5x share the variable part x.

Adding & Subtracting Expressions

To add or subtract expressions, combine like terms only. So 3x + 5x = 8x and 7a − 3a = 4a. Unlike terms cannot be combined.

Example 1: Simplify 3x + 5x.

8x.

Example 2: Simplify 7a − 3a.

4a.

Quick recap

Add or subtract only like terms.
Unlike terms stay separate.

✓ Quick check

Simplify: 4x + 2x.

4x + 2x = 6x.

Simplify: 9y − 5y.

9y − 5y = 4y.

Multiplication & Value of an Expression

Distributive Property: Multiply a number outside parentheses by each term inside.

a(b + c) = ab + ac

Factoring is the reverse of the distributive property — find the Greatest Common Factor (GCF) and pull it out.

ab + ac = a(b + c)

To factor, ask: what is the largest number/variable that divides all terms evenly?

DISTRIBUTIVE PROPERTY:

    3(2x + 5)
         |
    [split here]
    /          \
  3 x 2x  +  3 x 5
    |              |
   6x         +   15

Answer: 6x + 15

FACTORING (reverse):
  8x + 12
  GCF(8,12) = 4
  = 4(2x + 3)

Example 1: Expand 2(x + 3).

2x + 6.

Example 2: Expand x(x + 2).

x² + 2x.

Example 3: Simplify: 5(3x + 4)

5 x 3x + 5 x 4 = 15x + 20

Example 4: Simplify: 2(4y - 7)

2 x 4y - 2 x 7 = 8y - 14

Example 5: Factor: 8x + 12

GCF of 8 and 12 is 4. Factor out 4: 4(2x + 3). Check: 4 x 2x = 8x and 4 x 3 = 12.

Quick recap

Multiply a monomial into each term of the bracket.
Find the value by substituting for the variable.
Distribute to EVERY term inside the parentheses
Factoring = finding GCF and writing as a product
Check your factoring by distributing back
GCF must divide both the coefficient and the variable part

✓ Quick check

Expand: 3(x + 4).

3 × x + 3 × 4 = 3x + 12.

If x = 2, what is the value of 5x?

5 × 2 = 10.