3-answer.jpeg "(x-3)3 Answer")
Understanding (x-3)^3
(x-3)^3 represents the cube of the binomial (x-3). This means we are multiplying (x-3) by itself three times.
Expanding the Expression
To understand the answer, we need to expand the expression:
(x-3)^3 = (x-3)(x-3)(x-3)
We can expand this step by step:
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First, expand (x-3)(x-3): (x-3)(x-3) = x(x-3) - 3(x-3) = x^2 - 3x - 3x + 9 = x^2 - 6x + 9
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Now, multiply the result by (x-3): (x^2 - 6x + 9)(x-3) = x(x^2 - 6x + 9) - 3(x^2 - 6x + 9) = x^3 - 6x^2 + 9x - 3x^2 + 18x - 27
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Combine like terms: x^3 - 6x^2 + 9x - 3x^2 + 18x - 27 = x^3 - 9x^2 + 27x - 27
The Answer
Therefore, (x-3)^3 = x^3 - 9x^2 + 27x - 27. This is the expanded form of the expression.
Key Points to Remember
- Binomial: A polynomial with two terms (e.g., x-3).
- Cubing: Multiplying a number or expression by itself three times.
- Expansion: Breaking down an expression into simpler terms.
Understanding how to expand expressions like (x-3)^3 is a fundamental skill in algebra. It helps in solving equations, graphing functions, and understanding more complex mathematical concepts.