What should be added to x³ + 3x²y + 3xy² + y³ to get x³ + y³

Solution:

We have to add suitable terms to the given expression x³ + 3x²y + 3xy² + y³

to get x³ + y³

Let the term to be added be M.

Now, x³ + 3x²y + 3xy² + y³ + M = x³ + y³

Now, let us combine the like terms, and solve for M

3x²y + 3xy² + M = x³ + y³ - (x³ + y³)

3x²y + 3xy² + M = x³ - x³ + y³ - y³

By distributive property,

3x²y + 3xy² + M = (1 - 1)x³ + (1 - 1)y³

3x²y + 3xy² + M = (0)x³ + (0)y³

3x²y + 3xy² + M = 0

M = -(3x²y + 3xy²)

Therefore, M = -3x²y - 3xy²

✦ Try This: What should be added to 2x³ + 5x²y + 8xy² + 3y³ to get 2x³ + 2y³

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12

---

NCERT Exemplar Class 7 Maths Chapter 10 Problem 59 (a)

What should be added to x³ + 3x²y + 3xy² + y³ to get x³ + y³

Summary:

-3x²y - 3xy² should be added to x³ + 3x²y + 3xy² + y³ to get x³ + y³

---

☛ Related Questions:

• What should be added to 3pq + 5p²q² + p³ to get p³ + 2p²q² + 4pq
• What should be subtracted from 2x³ - 3x²y + 2xy² + 3y³ to get x³ - 2x²y + 3xy² + 4y³
• What should be subtracted from -7mn + 2m² + 3n² to get m² + 2mn + n²