Pascal's triangle and the Binomial Theorem

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Ari expands (2x + 1)^3. What is the coefficient of the x^2 term?

   12
2. 2.

   Bo expands (2x + 1)^4. What is the coefficient of the x^3 term?

   32
3. 3.

   Esme expands (2x + 1)^5. What is the coefficient of the x^4 term?

   80
4. 4.

   Kira wants the middle term of (x + y)⁸. Which is it?

   • 8x⁴y⁴
   • 70x⁴y⁴
   • 56x⁴y⁴
5. 5.

   Luz wants the constant term of (2x + 3)³. What is it?

   • 8
   • 27
   • 9
6. 6.

   Milo says (x + y)² = x² + y². Agree or disagree?

   • Disagree: it misses 2xy
   • Agree: square each part
   • Agree: it works for x = 0
7. 7.

   Noah says (x + 2)³ = x³ + 8. Agree or disagree?

   • Agree: cube each part
   • Disagree: try x = 1
   • Agree: 2³ is 8
8. 8.

   Pia says the coefficients of (x + y)⁷ add up to 14. Agree or disagree?

   • Disagree: they add to 128
   • Agree: 7 + 7 = 14
   • Agree: there are 14 terms
9. 9.

   What do all the coefficients of (2x + 1)⁴ add up to, Ren?

   • 32
   • 81
   • 16
10. 10.

    What do all the coefficients of (x − 1)⁵ add up to, Tala?

    • 32
    • 0
    • −32