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Questions and Answers
What is the result of expanding (x + 1)^3 using the cubic expansion formula?
What is the result of expanding (x + 1)^3 using the cubic expansion formula?
What is the formula for cubic expansion?
What is the formula for cubic expansion?
When expanding an algebraic expression using the cubic expansion formula, what should you do last?
When expanding an algebraic expression using the cubic expansion formula, what should you do last?
What is the pattern of coefficients in the cubic expansion formula?
What is the pattern of coefficients in the cubic expansion formula?
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What is the advantage of using the cubic expansion formula?
What is the advantage of using the cubic expansion formula?
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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
aand 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
aand work your way down when expanding. - Simplify your answer by combining like terms.
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Description
Learn about the formula and applications of cubic expansion in algebra, including examples and key points.
