How much is 21a³ – 17a² less than 89a³ – 64a² + 6a + 16?

Factorize completely: a^4 – 4a²b² + 4b^4

Calculate the volume of a cuboidal box whose dimensions are 5x, 3x², and 7x^4.

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.

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?

What should be subtracted from 2x³ – 3x²y + 2xy² + 3y³ to get x³ – 2x²y + 3xy² + 4y³?

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.

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.

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?

Using identities, evaluate 8.56 × 11.60

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.

The cost of one pen is (x + 3) rupees and the cost of one pencil is (x – 2) rupees. Find the total cost of 4 pens and 5 pencils.

Simplify: [(a + b)² – (a – b)²] ÷ (2ab)

Simplify: (x + y)² + (y + z)² + (z + x)² – (x² + y² + z²)

Factorize: (x² + 2x + 1) – (y² + 2y + 1)

If the sum of two numbers is (a + b) and their difference is (a – b), find the product of the numbers.

The side of a square is (x + 3). Find the expression for its area.

Find the value of (3x + 4)² when x = 2.

Simplify: (p + q)² – (p – q)²

Add: (3x² + 5x + 7) and (4x² – 2x + 3)

Find the value of 2x + 3y when x = 4 and y = 5.

Identify the coefficient of x² in the expression 5x² + 3x + 7

Subtract 5xy(x + y − 5) from x(6x² − 7y + 5) + xy(x + y)

What must be added to the sum of (x² − 4x + 7) and (2x² + 5x − 9) to get 0?

Rohan purchased a rectangular plot whose two adjacent sides are (y – 6x + 32 + 8) and (x – 2y – 5z – 8). He wants to put a wire fence twice around it. Find the total length of wire needed.

What will be the product if we multiply double of (x − 2/x) by triple of (x + 2/x)?

What should be subtracted from 3a + 7b – 10 to get –2a – 7b + 9?

Determine the product of (3a + 2b) and (9a² – 6ab + 4b²).

What is the sum of ab, a + b, and b + ab?

Simplify 7x²(3x – 9) + 3 and find its value for x = 4 and x = 6.

Find the value of x, if 10000x = (9982)² – (18)²

Find the value of (38² − 22²) / 16 using a suitable identity.

Verify that (11pq + 4q)² – (11pq – 4q)² = 176pq²

Multiply (x² + 2y) by (x³ – 2xy + y³) and find the value of the product for x = 1 and y = –1.

Multiply (6x² – 5x + 3) by (3x² + 7x – 3)

Multiply (3x² + 5y²) by (5x² – 3y²)

Subtract: (4x + 5) from (−3x + 7)

Add: 8x² + 7xy – 6y², 4x² – 3xy + 2y² and -4x² + xy – y²