Algebra 2 Binomial Theorem Quiz

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Questions and Answers

Find the coefficient of the 4th term in the expansion of (x + 3)^8.

1512

Find the coefficient of the 6th term in the expansion of (x + 2)^11.

14784

Find the 2nd term in the expansion of (x + 5)^7.

35x^6

Use the Binomial Theorem to expand (2x + 3)^4.

<p>16x^4 + 96x^3 + 216x^2 + 216x + 81</p> Signup and view all the answers

Use the Binomial Theorem to expand (3x + 1)^6.

<p>729x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1</p> Signup and view all the answers

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Study Notes

Binomial Theorem Key Concepts

  • The Binomial Theorem allows for the expansion of expressions in the form of (a + b)^n, where coefficients can be determined using combinations.
  • Each term in the expansion can be represented as C(n, k)a^(n-k)b^k, where C(n, k) is the binomial coefficient.

Example Problems

  • 4th Term Coefficient of (x + 3)^8

    • Coefficient calculated: 1512
    • Term structure follows the binomial expansion rules.
  • 6th Term Coefficient of (x + 2)^11

    • Coefficient determined: 14784
    • Utilizes the formula for a specific term in the expansion.
  • 2nd Term of (x + 5)^7

    • Result is 35x^6
    • The second term is calculated using binomial expansion principles.

Expansions Using Binomial Theorem

  • Expansion of (2x + 3)^4

    • Resulting expression: 16x^4 + 96x^3 + 216x^2 + 216x + 81
    • Each term arises from applying the binomial theorem correctly to the coefficients and powers.
  • Expansion of (3x + 1)^6

    • Resulting expression: 729x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1
    • Each term includes the corresponding coefficient and powers of x as per binomial expansion.

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