Last reviewed: 7 November 2026
Updated November 2026. These Grade 8 algebraic expressions notes cover factorising by taking out common factors, simplifying algebraic fractions, and evaluating expressions by substituting numbers. To factorise, find the highest common factor of all the terms and write it outside a bracket: 6x + 9 = 3(2x + 3). To evaluate, replace each letter with its value and follow the order of operations.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 8 maths topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Algebraic expressions is a sub-strand under Algebra in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners factorise algebraic expressions, simplify algebraic fractions, and evaluate expressions by substituting numerical values. The design is listed on the KICD Grade Eight curriculum designs page. Factorising quadratic expressions belongs to later work and is not covered here.
Like and Unlike Terms
Like terms have exactly the same letters with the same powers: 3x and 7x are like terms; 3x and 3x² are not. Only like terms can be added or subtracted. 5a + 2b − 3a + b = 2a + 3b.
Factorising by Common Factors
Factorising is the reverse of expanding brackets. The method, finding the greatest common factor, is set out in OpenStax Elementary Algebra’s section on greatest common factor.
- Find the highest common factor (HCF) of the numbers.
- Find the letters common to every term, using the lowest power of each.
- Write the HCF outside the bracket and divide each term by it.
- Check by expanding.
Worked examples
- 12y − 8 = 4(3y − 2).
- 5x² + 15x = 5x(x + 3).
- 4a²b − 10ab² = 2ab(2a − 5b). Check: 2ab × 2a = 4a²b and 2ab × 5b = 10ab².
Taking out only part of the common factor, such as writing 12y − 8 = 2(6y − 4), is not fully factorised. The terms in the bracket should have no common factor left.
Simplifying Algebraic Fractions
Cancelling after factorising
You may only cancel factors, never single terms joined by + or −.
Example: (3x + 6) ÷ (x + 2). Factorise the top: 3(x + 2). Then 3(x + 2) ÷ (x + 2) = 3 (for x ≠ −2). Cancelling the x’s in (x + 6)/x to get 6 is wrong, because x is a term, not a factor, of the top.
Adding and subtracting algebraic fractions
Use a common denominator, just as with number fractions.
Example: 2a/3 + a/4. The LCM of 3 and 4 is 12: 8a/12 + 3a/12 = 11a/12.
Example: (x + 1)/2 − (x − 3)/5. Common denominator 10: [5(x + 1) − 2(x − 3)] ÷ 10 = (5x + 5 − 2x + 6) ÷ 10 = (3x + 11)/10. Watch the sign: −2 × −3 = +6.
Evaluating Expressions by Substitution
Replace each letter with its value, using brackets around negative numbers, then work out the answer in the correct order.
Worked example
Evaluate 3x² − 2y when x = −2 and y = 5.
- 3(−2)² − 2(5)
- (−2)² = 4, so 3 × 4 = 12.
- 12 − 10 = 2.
Writing −2² = −4 is a frequent error; the brackets make the square apply to −2.
Real-life example
A taxi fare in this made-up example is F = 150 + 45k shillings, where k is the number of kilometres. For k = 8: F = 150 + 45 × 8 = 150 + 360 = KSh 510.
Original Practice Questions With Worked Answers
- Factorise 14m + 21. 7(2m + 3).
- Factorise 6p²q − 9pq. 3pq(2p − 3).
- Simplify (5y − 10) ÷ (y − 2). 5(y − 2) ÷ (y − 2) = 5.
- Simplify x/2 + 2x/5. 5x/10 + 4x/10 = 9x/10.
- Evaluate 2a + b² when a = 3 and b = −4. 6 + 16 = 22.
Cover the answers and attempt each question first. For timed practice, use the Grade 8 revision papers or the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
How do you factorise an algebraic expression in Grade 8?
Find the highest common factor of all the terms, write it outside a bracket, and divide each term by it to fill the bracket.
When can I cancel in an algebraic fraction?
Only when the same factor multiplies the whole numerator and the whole denominator. Factorise first, then cancel.
How do you evaluate an algebraic expression?
Substitute the given values for the letters, using brackets for negative numbers, and calculate in the correct order of operations.
What are like terms?
Terms with exactly the same letters raised to the same powers, such as 4xy and −2xy.