(2x%2B7)(x%2B1).jpeg "(2x-3)(2x+7)(x+1)")
Expanding and Simplifying (2x-3)(2x+7)(x+1)
This expression involves multiplying three binomials together. We can do this by expanding the expression step by step.
Step 1: Expanding the first two binomials
First, we will multiply the first two binomials, (2x-3) and (2x+7), using the FOIL method:
- First: 2x * 2x = 4x²
- Outer: 2x * 7 = 14x
- Inner: -3 * 2x = -6x
- Last: -3 * 7 = -21
Combining the terms, we get: 4x² + 14x - 6x - 21 = 4x² + 8x - 21
Step 2: Expanding the result with the remaining binomial
Now, we will multiply the result from step 1 (4x² + 8x - 21) by the remaining binomial (x+1). We can do this by distributing each term of the trinomial over the binomial:
- 4x² * (x+1) = 4x³ + 4x²
- 8x * (x+1) = 8x² + 8x
- -21 * (x+1) = -21x - 21
Finally, we combine all the terms: 4x³ + 4x² + 8x² + 8x - 21x - 21 = 4x³ + 12x² - 13x - 21
Final Result
Therefore, the expanded and simplified form of (2x-3)(2x+7)(x+1) is 4x³ + 12x² - 13x - 21.