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MathematicsClass 8Algebraic Expressions and Identities

Algebraic Expressions and Identities | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 4 min read

Algebraic Expressions and Identities – this guide gives you a concise, exam-ready overview of Algebraic Expressions and Identities from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Addition and Subtraction of Algebraic Expressions

Adding and subtracting algebraic expressions involves combining like terms. When adding two expressions, we group the like terms together and add their coefficients. Similarly, subtraction involves grouping like terms and subtracting their coefficients.

For example, to add (3x + 5y) and (4x - 2y), we combine like terms: (3x + 4x) + (5y - 2y) = 7x + 3y.

The steps to add or subtract algebraic expressions are: 1. Remove parentheses by applying the distributive property if necessary. 2. Identify like terms. 3. Add or subtract the coefficients of like terms. 4. Write the simplified expression.

It is important to be careful with signs, especially during subtraction. For example, subtracting (2x - 3y) from (5x + y) means: (5x + y) - (2x - 3y) = 5x + y - 2x + 3y = (5x - 2x) + (y + 3y) = 3x + 4y.

This section also introduces the concept of zero polynomial, which is the expression 0, representing no terms.

Mastering addition and subtraction of algebraic expressions is essential for simplifying expressions and solving algebraic equations.

📊 Diagram: Diagram showing addition of two algebraic expressions with like terms grouped and combined.

🧪 Activity: Activity: Perform addition and subtraction on given algebraic expressions and verify results.

🔗 Connection: This section leads to 'Multiplication of Algebraic Expressions' where operations become more complex involving distributive property.

Frequently asked questions

1. Add the following. (i) $ab - bc, bc - ca, ca - ab$ (ii) $a - b + ab, b - c + bc, c - a + ac$ (iii) $2p^{2}q^{2} - 3pq + 4,5 + 7pq - 3p^{2}q^{2}$ (iv) $l^{2} + m^{2}, m^{2} + n^{2}, n^{2} + l^{2},$ $$ 2lm + 2mn + 2nl $$

Solution:

(i) Add: (ab - bc) + (bc - ca) + (ca - ab) = ab - bc + bc - ca + ca - ab = (ab - ab) + (-bc + bc) + (-ca + ca) = 0

(ii) Add: (a - b + ab) + (b - c + bc) + (c - a + ac) = a - b + ab + b - c + bc + c - a + ac = (a - a) + (-b + b) + (-c + c) + ab + bc + ac = ab + bc + ac

(iii) Add: (2p^{2}q^{2} - 3pq + 4) + (5 + 7pq - 3p^{2}q^{2}) = 2p^{2}q^{2} - 3pq + 4 + 5 + 7pq - 3p^{2}q^{2} = (2p^{2}q^{2} - 3p^{2}q^{2}) + (-3pq + 7pq) + (4 + 5) = (-p^{2}q^{2}) + (4pq) + 9

(iv) Add: (l^{2} + m^{2})

2. (a) Subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$ (b) Subtract $3xy + 5yz - 7zx$ from $5xy - 2yz - 2zx + 10xyz$ (c) Subtract $4p^{2}q - 3pq + 5pq^{2} - 8p + 7q - 10$ from $$ 18 - 3p - 11q + 5pq - 2pq^{2} + 5p^{2}q $$

Solution:

(a) Subtracting (4a - 7ab + 3b + 12) from (12a - 9ab + 5b - 3): = (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12) = 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12 = (12a - 4a) + (-9ab + 7ab) + (5b - 3b) + (-3 - 12) = 8a - 2ab + 2b - 15

(b) Subtracting (3xy + 5yz - 7zx) from (5xy - 2yz - 2zx + 10xyz): = (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx) = 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx = (5xy - 3xy) + (-2yz - 5yz) + (-2zx + 7zx) + 10xyz = 2xy - 7yz + 5zx + 10xyz

(c) Subtracting (4p^{2}q -

TRY THESE Find $4x imes 5y imes 7z$ First find $4x imes 5y$ and multiply it by $7z$; or first find $5y imes 7z$ and multiply it by $4x$. Is the result the same? What do you observe? Does the order in which you carry out the multiplication matter?

Solution:

First method: 4x × 5y = 20xy Then, 20xy × 7z = 140xyz

Second method: 5y × 7z = 35yz Then, 4x × 35yz = 140xyz

Observation: The result is the same (140xyz) in both methods.

Conclusion: The order of multiplication does not matter (commutative property of multiplication).

Example 3: Complete the table for area of a rectangle with given length and breadth. Solution: | length | breadth | area | |--------|---------|-------| | 3x | 5y | 3x × 5y = 15xy | | 9y | 4y² | ... | | 4ab | 5bc | ... | | 2l²m | 3lm² | ... |

Solution:

Area = length × breadth

For 9y and 4y²: Area = 9y × 4y² = 36y^{3}

For 4ab and 5bc: Area = 4ab × 5bc = 20ab^{2}c

For 2l^{2}m and 3lm^{2}: Area = 2l^{2}m × 3lm^{2} = 6l^{3}m^{3}

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