(2x%5E3%2B4x%5E2-5).jpeg "(3x-1)(2x^3+4x^2-5)")
Expanding the Expression (3x - 1)(2x³ + 4x² - 5)
This expression involves multiplying a binomial (3x - 1) with a trinomial (2x³ + 4x² - 5). We can expand this expression using the distributive property, which states that the product of a sum and a number is equal to the sum of the products of the number and each term of the sum.
Step 1: Distribute the first term of the binomial (3x)
- 3x multiplied by 2x³ gives 6x⁴
- 3x multiplied by 4x² gives 12x³
- 3x multiplied by -5 gives -15x
Step 2: Distribute the second term of the binomial (-1)
- -1 multiplied by 2x³ gives -2x³
- -1 multiplied by 4x² gives -4x²
- -1 multiplied by -5 gives 5
Step 3: Combine the terms
Now, we have the following terms:
6x⁴ + 12x³ - 15x - 2x³ - 4x² + 5
Combining the like terms, we get the final expanded expression:
6x⁴ + 10x³ - 4x² - 15x + 5
Therefore, the expanded form of (3x - 1)(2x³ + 4x² - 5) is 6x⁴ + 10x³ - 4x² - 15x + 5.