Questions Related to Algebra
Updated on November 1, 2025 | By Learnzy Academy
Q1. Factorize completely: a^4 – 4a²b² + 4b^4
Q2. Calculate the volume of a cuboidal box whose dimensions are 5x, 3x², and 7x^4.
Step 1: Formula for volume of a cuboid
Volume = length × breadth × height
Step 2: Substitute the given values
Volume = (5x) × (3x²) × (7x⁴)
Step 3: Multiply the constants and powers of x
= (5 × 3 × 7) × (x × x² × x⁴)
= 105 × x⁷
Final Answer: Volume = 105x⁷
Q3. Shiv works in a mall and gets paid Rs 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
Money for last week = 50 × 7 = 350
Money for this week = 50 × x = 50x
Total money = 350 + 50x
Final Answer: 50x + 350
Q4. Rohan's mother gave him Rs 3xy² and his father gave him Rs 5(xy² + 2). Out of this total money, he spent Rs (10 – 3xy²) on his birthday party. How much money is left with him?
Total money received = 3xy² + 5(xy² + 2)
= 3xy² + 5xy² + 10
= 8xy² + 10
Money left = (8xy² + 10) – (10 – 3xy²)
= 8xy² + 10 – 10 + 3xy²
= 11xy²
Final Answer: ₹11xy²
Q5. What should be subtracted from 2x³ – 3x²y + 2xy² + 3y³ to get x³ – 2x²y + 3xy² + 4y³?
Let the required expression be A.
Then,
(2x³ – 3x²y + 2xy² + 3y³) – A = (x³ – 2x²y + 3xy² + 4y³)
So,
A = (2x³ – 3x²y + 2xy² + 3y³) – (x³ – 2x²y + 3xy² + 4y³)
= 2x³ – 3x²y + 2xy² + 3y³ – x³ + 2x²y – 3xy² – 4y³
= (2x³ – x³) + (–3x²y + 2x²y) + (2xy² – 3xy²) + (3y³ – 4y³)
= x³ – x²y – xy² – y³
Final Answer: x³ – x²y – xy² – y³
Q6. How much is 21a³ – 17a² less than 89a³ – 64a² + 6a + 16?
89a³ – 64a² + 6a + 16) – (21a³ – 17a²)
=> 89a³ – 64a² + 6a + 16 – 21a³ + 17a²
=> (89a³ – 21a³) + (–64a² + 17a²) + 6a + 16
= > 68a³ – 47a² + 6a + 16
Final Answer: 68a³ – 47a² + 6a + 16
Q7. Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.
Area of rectangular plot = x × y = xy
Area of triangular part sold = ½ × base × height = ½ × y × z = ½yz
Area of remaining part = Total area − Area sold
= xy − ½yz
Final Answer: xy − ½yz
Q8. Sonu and Raj have to collect different kinds of leaves for a science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time, Sonu loses 3 leaves and Raj collects 2x more leaves. Write an algebraic expression to find the total number of leaves collected by both of them.
Leaves with Sonu = 12 − 3 = 9
Leaves with Raj = x + 2x = 3x
Total leaves = (9) + (3x) = 3x + 9
Final Answer: 3x + 9
Q9. Amisha has a square plot of side m and another triangular plot with base and height each equal to m. What is the total area of both plots?
Area of square = m × m = m²
Area of triangle = ½ × base × height = ½ × m × m = ½m²
Total area = m² + ½m² = 3/2 m²
Final Answer: 3/2 m²
Q10. Using identities, evaluate 8.56 × 11.60
Let 8.56 = (10 − 1.44) and 11.60 = (10 + 1.60)
Using the identity (a + b)(a + c) = a² + a(b + c) + bc
Here, a = 10, b = −1.44, c = 1.60
8.56 × 11.60 = 10² + 10(−1.44 + 1.60) + (−1.44)(1.60)
= 100 + 10(0.16) − 2.304
= 100 + 1.6 − 2.304
= 99.296
Final Answer: 99.296
Q11. The area of a rectangle is uv, where u is the length and v is the breadth. If the length is increased by 5 units and the breadth is decreased by 3 units, find the new area of the rectangle.
New length = u + 5
New breadth = v − 3
New area = (u + 5)(v − 3)
= uv − 3u + 5v − 15
Final Answer: uv − 3u + 5v − 15