(x%2B3)(x%2B3).jpeg "(x+3)(x+3)(x+3)")
Expanding and Simplifying (x+3)(x+3)(x+3)
This expression represents the product of three identical binomials: (x+3). To simplify it, we can use the distributive property of multiplication multiple times.
Step 1: Expand the first two binomials
First, we'll expand the product of the first two binomials: (x+3)(x+3)
- FOIL method: We can use the FOIL method (First, Outer, Inner, Last) for this.
- First: x * x = x²
- Outer: x * 3 = 3x
- Inner: 3 * x = 3x
- Last: 3 * 3 = 9
- Combining like terms: x² + 3x + 3x + 9 = x² + 6x + 9
Now we have: (x² + 6x + 9)(x+3)
Step 2: Expand the entire expression
Next, we'll distribute the (x+3) term to each term within the trinomial (x² + 6x + 9).
- x * (x² + 6x + 9): This gives us x³ + 6x² + 9x
- 3 * (x² + 6x + 9): This gives us 3x² + 18x + 27
Step 3: Combine like terms
Now we have: x³ + 6x² + 9x + 3x² + 18x + 27
Combining like terms, we get: x³ + 9x² + 27x + 27
Conclusion
Therefore, the simplified expression for (x+3)(x+3)(x+3) is x³ + 9x² + 27x + 27.
This process demonstrates how to expand and simplify expressions involving repeated binomials.