Cubic Expansion Formula and Examples
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Questions and Answers

What is the result of expanding (x + 1)^3 using the cubic expansion formula?

  • x^3 + 3x^2 + 2x + 1
  • x^3 + x^2 + x + 1
  • x^3 + 2x^2 + x + 1
  • x^3 + 3x^2 + 3x + 1 (correct)

    • What is the formula for cubic expansion?

  • (a + b)^3 = a^3 + a^2b + ab^2 + b^3
  • (a + b)^3 = a^3 + 2a^2b + 2ab^2 + b^3
  • (a + b)^3 = a^3 + 4a^2b + 4ab^2 + b^3
  • (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (correct)

    • When expanding an algebraic expression using the cubic expansion formula, what should you do last?

  • Rearrange the terms in alphabetical order
  • Simplify the expression by combining like terms (correct)
  • Cube each term and multiply by the correct coefficient
  • Factor out the greatest common factor

    • What is the pattern of coefficients in the cubic expansion formula?

    <p>one, three, three, one</p> Signup and view all the answers

    What is the advantage of using the cubic expansion formula?

    <p>It can be used to expand any algebraic expression of the form (a + b)^3</p> Signup and view all the answers

    Study Notes

    Cubic Expansion

    Cubic expansion is a method of expanding algebraic expressions of the form (a + b)^3.

    Formula

    The formula for cubic expansion is:

    (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

    This formula can be used to expand any algebraic expression of the form (a + b)^3.

    Example

    Expand (x + 2)^3 using the cubic expansion formula:

    (x + 2)^3 = x^3 + 3x^2(2) + 3x(2)^2 + 2^3 = x^3 + 6x^2 + 12x + 8

    Key Points

    • The formula for cubic expansion is (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
    • The formula can be used to expand any algebraic expression of the form (a + b)^3.
    • When using the formula, remember to cube each term and multiply by the correct coefficient (1, 3, 3, or 1).

    Tips and Tricks

    • To remember the formula, try thinking of the pattern: "one, three, three, one" for the coefficients.
    • When expanding, start with the highest power of a and work your way down.
    • Simplify your answer by combining like terms.

    Cubic Expansion

    • Cubic expansion is a method used to expand algebraic expressions of the form (a + b)^3.

    Formula

    • The formula for cubic expansion is (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.

    Expanding Expressions

    • The formula can be used to expand any algebraic expression of the form (a + b)^3.
    • Example: (x + 2)^3 = x^3 + 3x^2(2) + 3x(2)^2 + 2^3 = x^3 + 6x^2 + 12x + 8.

    Key Points

    • Cube each term and multiply by the correct coefficient (1, 3, 3, or 1) when using the formula.
    • Remember the formula pattern: "one, three, three, one" for the coefficients.

    Tips and Tricks

    • Start with the highest power of a and work your way down when expanding.
    • Simplify your answer by combining like terms.

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    Quiz Team

    Description

    Learn about the formula and applications of cubic expansion in algebra, including examples and key points.

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