Worksheet on Algebraic Expressions for Class 7

Master mathematical expressions with our algebraic expressions printable grade 7 practice questions. This detailed practice sheet teaches students to work with variables, coefficients and algebraic operations through systematic methods and problem solving activities. Kids will understand expression simplification and evaluation perfectly for advanced mathematics. Download free Class 7 algebraic expressions pdf worksheet, perfect for regular practice.

Solved Questions on Algebraic Expressions

1. What is the area of a square field if the length of each side is (ax + by − c) units?

a) [a²x² + b²y² + 2abxy + 2acx − 2bcy + c²] sq. units
b) [a²x² + b²y² + 2abxy − 2acx − 2bcy + c²] sq. units
c) [a²x² + b²y² + 2abxy − 2acx + 2bcy + c²] sq. units
d) [a²x² + b²y² − 2abxy + 2acx − 2bcy + c²] sq. units

Answer: b) [a²x² + b²y² + 2abxy − 2acx − 2bcy + c²] sq. units

Explanation: Length of each side = (ax + by − c) units

Area of a square field = (Length of each side)²

= (ax + by − c)²
= (ax + by − c) ×  (ax + by − c)
= ax (ax + by − c) + by (ax + by − c) − c (ax + by − c)
= a²x² + abxy − acx + abxy + b²y² − bcy − acx − bcy + c²
= a²x² + b²y² + abxy + abxy − acx − acx − bcy − bcy + c²
= a²x² + b²y² + (1 + 1)abxy − (1 + 1)acx − (1 + 1)bcy + c²
= [a²x² + b²y² + 2abxy − 2acx − 2bcy + c²] sq. units

2. If the length of a rectangle is (4x – 13y) units and the perimeter is (8x + 128y) units, what is the breadth of the rectangle?

a) 51y units
b) (x + 51y) units
c) 77y units
d) (x + 77y) units

Answer: c) 77y units

Explanation: Perimeter of the rectangle = (8x + 128y) units

3. In an auditorium, (p + t) seats are arranged in (p − t) rows. How many seats are there in the auditorium?

a) p² − 2pt − t²
b) p² + 2pt − t²
c) p² − t²
d) t² − p²

Answer: c) p² − t²

Explanation: Number of seats = p + t

Number of rows = p − t

Total number of seats = Number of seats × Number of rows

= (p + t)(p − t) 
= p(p − t) + t (p − t)
= p² − pt + pt − t²
= p² − t²

4. What is the cost of (q − 3) cups if the cost of q cups is $(11q³ − 9pq)?

a) $(11q³ + 33q² − 9pq + 27p)
b) $(11q³ − 33q² + 9pq + 27p)
c) $(11q³ + 33q² − 9pq + 27p)
d) $(11q³ − 33q² − 9pq + 27p)

Answer: d) $(11q³ − 33q² − 9pq  + 27p)

Explanation: Cost of q cups = $(11q³ − 9pq)
Cost of 1 cup = $[(11q³ − 9pq)/q] = $(11q² − 9p)
Cost of (q − 3) cups =  (q − 3) × (11q² − 9p)
= q × (11q² − 9p) − 3 × (11q² − 9p)
= 11q³ − 9pq − 33q²  + 27p
= $(11q³ − 33q² − 9pq  + 27p)

5. What must be added to 3y³ – 5y² + 4y + 7 to get 7y³ + 9y – 13?

a) y(4y² – 5y – 5) + 20 
b) y(4y² + 5y + 5) – 20 
c) y(4y² + 5y – 5) – 20 
d) y(4y² + 5y – 5) + 20 

Answer: b) y(4y² + 5y  + 5) – 20  

Explanation: Required algebraic expressions = (7y³ + 9y – 13) − (3y³ – 5y² + 4y + 7)

= 7y³ + 9y – 13 − 3y³ + 5y² − 4y − 7
= 7y³ − 3y³ + 5y²  + 9y − 4y – 13 − 7
= 4y³ + 5y²  + 5y – 20
= y(4y² + 5y  + 5) – 20