%5E3-simplify.jpeg "(2x-7)^3 Simplify")
Simplifying (2x - 7)³
This expression involves cubing a binomial, which means multiplying the binomial by itself three times. Let's break down the steps:
Expanding the Expression
- Write out the expression: (2x - 7)³ = (2x - 7)(2x - 7)(2x - 7)
- Multiply the first two binomials:
- Use the FOIL method (First, Outer, Inner, Last) or any other method you prefer.
- (2x - 7)(2x - 7) = 4x² - 14x - 14x + 49 = 4x² - 28x + 49
- Multiply the result by the remaining binomial:
- (4x² - 28x + 49)(2x - 7) = 8x³ - 56x² + 98x - 28x² + 196x - 343
- Combine like terms: 8x³ - 84x² + 294x - 343
Simplified Expression
Therefore, the simplified form of (2x - 7)³ is 8x³ - 84x² + 294x - 343.
Key Points
- FOIL method: A helpful tool for multiplying binomials.
- Combining like terms: Essential for simplifying polynomial expressions.
- Practice makes perfect: Familiarize yourself with binomial expansions and simplifying techniques.