ALGEBRAIC EXPRESSIONS & IDENTITIES — MASTER
ADITYA
NOTES
1. What is Algebraic Expression
A combo-pack of numbers + variables + operations.
Form looks like:
a+b
2x – 5
4x² + 3xy – 7
A term = one unit separated by + or −.
Coefficient = number multiplying a variable.
Constant = number without any variable.
Opinion: Once you see expressions as objects, not random letters, the game becomes easy.
2. Types of Expressions
(A) Monomial
1 term
Example: 5x, −3y², 2abc
(B) Binomial
2 terms
Example: x + 3, 2x² − 5y
(C) Polynomial (Class-8 level)
Sum of many terms
Example: 3x² + 2x − 7
3. Like & Unlike Terms
Like terms have same variable and power. Add/subtract directly.
Example:
3x² + 5x² = 8x² (clean)
But 3x + 3x² (don’t add, different powers)
4. Addition & Subtraction
Just combine like terms, don’t touch unlike ones.
Example:
(4x + 5) + (2x − 7)
= 4x + 2x + 5 − 7
= 6x − 2
Trap: Signs change when subtracting.
Example:
(7x − 2y) − (5x + 3y)
= 7x − 2y − 5x − 3y
= 2x − 5y
5. Multiplication of Expressions
Three game modes:
(A) Constant × Variable
6 × 2x = 12x
(−3) × (4xy) = −12xy
(B) Variable × Variable
ADITYA
NOTES
1. What is Algebraic Expression
A combo-pack of numbers + variables + operations.
Form looks like:
a+b
2x – 5
4x² + 3xy – 7
A term = one unit separated by + or −.
Coefficient = number multiplying a variable.
Constant = number without any variable.
Opinion: Once you see expressions as objects, not random letters, the game becomes easy.
2. Types of Expressions
(A) Monomial
1 term
Example: 5x, −3y², 2abc
(B) Binomial
2 terms
Example: x + 3, 2x² − 5y
(C) Polynomial (Class-8 level)
Sum of many terms
Example: 3x² + 2x − 7
3. Like & Unlike Terms
Like terms have same variable and power. Add/subtract directly.
Example:
3x² + 5x² = 8x² (clean)
But 3x + 3x² (don’t add, different powers)
4. Addition & Subtraction
Just combine like terms, don’t touch unlike ones.
Example:
(4x + 5) + (2x − 7)
= 4x + 2x + 5 − 7
= 6x − 2
Trap: Signs change when subtracting.
Example:
(7x − 2y) − (5x + 3y)
= 7x − 2y − 5x − 3y
= 2x − 5y
5. Multiplication of Expressions
Three game modes:
(A) Constant × Variable
6 × 2x = 12x
(−3) × (4xy) = −12xy
(B) Variable × Variable
