Evaluation of Algebraic Expressions

Evaluating algebraic expressions means finding the value of an expression by replacing each variable with a given number. .

(i) 4m − 9 for m = −3

= 4 × (−3) − 9

= −12 − 9

= −21

(ii) 5p + 24 for p = −3

= 5 × (−3) + 24

= −15 + 24

= 9 

If x = 2 and y = 3, evaluate:
Solution:

1. xy = x × y = 2 × 3 = 6
   
   
2. 5x²y = 5 × x × x × y = 5 × 2 × 2 × 3 = 60
   
   
3. 5y² = 5 × y × y = 5 × 3 × 3 = 45
   
   
4. (5y)² = 5y × 5y = 5 × 5 × y × y = 25 × 3 × 3 = 225

If a = 3 and b = −4, evaluate 2a² − b².
Solution:

2a² − b² = (2 × a × a) − (b × b)

= (2 × 3 × 3) − (−4 × −4)

= 18 − (16)

= 18 − 16

= 2 

• Always write down the substituted expression first.

• Compute exponents before other operations.

• Simplify one step at a time for clarity.

Common Errors

• Forgetting negatives: −3 × 4 ≠ −3 + 4

• Wrong order: Adding before multiplying.

• Skipping steps: Leads to sign and calculation mistakes.