Answer:
12x^3 - 14x^2 + 18x + 14
Step-by-step explanation:
To multiply the expressions (4x + 2) and (3x^2 - 5x + 7), you can use the distributive property and multiply each term in the first expression by each term in the second expression. Here's the step-by-step process:
(4x + 2) (3x^2 - 5x + 7)
First, distribute the first term of the first expression (4x) to each term in the second expression:
4x * 3x^2 + 4x * (-5x) + 4x * 7
This simplifies to:
12x^3 - 20x^2 + 28x
Next, distribute the second term of the first expression (2) to each term in the second expression:
2 * 3x^2 + 2 * (-5x) + 2 * 7
This simplifies to:
6x^2 - 10x + 14
Finally, combine the results from the two distributions:
12x^3 - 20x^2 + 28x + 6x^2 - 10x + 14
Combining like terms:
12x^3 - 20x^2 + 6x^2 + 28x - 10x + 14
Simplifying further:
12x^3 - 14x^2 + 18x + 14
So, the product of (4x + 2) and (3x^2 - 5x + 7) is 12x^3 - 14x^2 + 18x + 14.
