Answer :
To simplify the given expression [tex]\(\left(-x^2 + x\right) + \left(4x^2 - x - 1\right)\)[/tex], we need to follow these steps:
1. Combine like terms by grouping the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms separately.
The given expression is:
[tex]\[ \left(-x^2 + x\right) + \left(4x^2 - x - 1\right) \][/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ -x^2 + 4x^2 = 3x^2 \][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
[tex]\[ x - x = 0 \][/tex]
4. Combine the constant terms:
[tex]\[ -1 \][/tex]
5. Putting it all together, we get:
[tex]\[ 3x^2 + 0x - 1 \][/tex]
Simplifying the term [tex]\(0x\)[/tex], the expression becomes:
[tex]\[ 3x^2 - 1 \][/tex]
So, the simplified form of the expression is:
[tex]\[ 3x^2 - 1 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{3x^2 - 1} \][/tex]
Thus, the correct choice is:
[tex]\[ \text{B. } 3x^2 - 1 \][/tex]
1. Combine like terms by grouping the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms separately.
The given expression is:
[tex]\[ \left(-x^2 + x\right) + \left(4x^2 - x - 1\right) \][/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ -x^2 + 4x^2 = 3x^2 \][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
[tex]\[ x - x = 0 \][/tex]
4. Combine the constant terms:
[tex]\[ -1 \][/tex]
5. Putting it all together, we get:
[tex]\[ 3x^2 + 0x - 1 \][/tex]
Simplifying the term [tex]\(0x\)[/tex], the expression becomes:
[tex]\[ 3x^2 - 1 \][/tex]
So, the simplified form of the expression is:
[tex]\[ 3x^2 - 1 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{3x^2 - 1} \][/tex]
Thus, the correct choice is:
[tex]\[ \text{B. } 3x^2 - 1 \][/tex]
