Add or subtract.
(4x2 – 2x – 1) – (–3x3 + 2)
A. –3x3 + 4x2 – 2x + 1
B. –3x3 + 4x2 – 2x – 3
C. 3x3 + 4x2 – 2x + 1
D. 3x3 + 4x2 – 2x – 3
B. –3x3 + 4x2 – 2x – 3
To solve this problem, we need to simplify the expression by subtracting the second quantity from the first.
The expression is:
(4x^2 – 2x – 1) – (–3x^3 + 2)
First, let's distribute the negative sign to the second quantity by changing the signs of all its terms:
(4x^2 – 2x – 1) + (3x^3 - 2)
Now we can combine like terms by adding or subtracting coefficients of the same variables:
4x^2 – 2x – 1 + 3x^3 - 2
Next, we arrange the terms in descending order of the exponent of x:
3x^3 + 4x^2 - 2x - 1 - 2
Simplifying further, we add or subtract the coefficients:
3x^3 + 4x^2 - 2x - 3
Therefore, the correct answer is option B:
-3x^3 + 4x^2 - 2x - 3
To add or subtract the given expressions, we need to distribute the negative sign to the terms in the second expression and then combine like terms.
The first expression is: 4x^2 - 2x - 1
The second expression after distributing the negative sign is: -(-3x^3 + 2) = 3x^3 - 2
Now, we can combine like terms:
4x^2 - 2x - 1 - (3x^3 - 2)
= 4x^2 - 2x - 1 - 3x^3 + 2
= -3x^3 + 4x^2 - 2x + 1
Therefore, the answer is A. -3x^3 + 4x^2 - 2x + 1.