Pascal's triangle and the Binomial Theorem

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Bo expands (x + y)^8. What is the coefficient of the x^6y² term?

   28
2. 2.

   Esme expands (x + y)^10. What is the coefficient of the x^8y² term?

   45
3. 3.

   Jun expands (x + 1)⁴. Which is right?

   • x⁴ + 4x³ + 4x² + 4x + 1
   • x⁴ + 1
   • x⁴ + 4x³ + 6x² + 4x + 1
4. 4.

   Kira expands (x − y)³. Which is right?

   • x³ − 3x²y − 3xy² − y³
   • x³ − 3x²y + 3xy² − y³
   • x³ + 3x²y + 3xy² − y³
5. 5.

   Which row of the triangle does Milo need for (x + y)⁶?

   • Row 5: 1, 5, 10, 10, 5, 1
   • Row 7, the seventh row from the top
   • Row 6: 1, 6, 15, 20, 15, 6, 1
6. 6.

   In (x + y)⁶, what coefficient does Noah find for x³y³?

   • 15
   • 20
   • 6
7. 7.

   Why does each row of Pia's triangle read the same from both ends?

   • x and y are equal numbers
   • Picking k is like leaving n − k
   • Each row adds up to the same total
8. 8.

   Ren expands (x − 2)³ = x³ − 6x² + 12x − 8. What pattern do the signs make?

   • −, −, −, −
   • +, +, +, −
   • +, −, +, −
9. 9.

   What is the constant term of (x − 2)³ in Tala's expansion?

   • 8
   • −6
   • −8
10. 10.

    Zee expands (x − 1)⁴. What is the coefficient of x?

    • −4
    • −1
    • 4