%5E3-expand-and-simplify.jpeg "(x+3)^3 Expand And Simplify")
Expanding and Simplifying (x + 3)³
In algebra, we often encounter expressions like (x + 3)³. This represents the product of (x + 3) with itself three times. Expanding and simplifying such expressions is a fundamental skill. Here's how we do it:
Understanding the Concept
(x + 3)³ means (x + 3) * (x + 3) * (x + 3)
To expand this, we can use the distributive property (also known as FOIL) multiple times.
Step-by-Step Expansion
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Expand the first two factors: (x + 3) * (x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9
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Multiply the result by the remaining (x + 3): (x² + 6x + 9) * (x + 3) = x³ + 3x² + 6x² + 18x + 9x + 27
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Combine like terms: x³ + 9x² + 27x + 27
Simplified Form
Therefore, the expanded and simplified form of (x + 3)³ is x³ + 9x² + 27x + 27.
Key Points
- FOIL: The acronym FOIL (First, Outer, Inner, Last) is a helpful mnemonic for remembering the distributive property when multiplying binomials.
- Patterns: Expanding expressions like (x + 3)³ can be done using the binomial theorem, which reveals a pattern in the coefficients.
- Practice: Expanding and simplifying expressions is essential for various algebraic manipulations. Practice with different examples to gain proficiency.