Answer :
To simplify the expression [tex]\((2x^3 + x^2 - 4x) - (9x^3 - 3x^2)\)[/tex], follow these steps:
1. Distribute the Negative Sign:
The expression is given as a subtraction of two groups of terms. First, distribute the negative sign across the second set of parentheses:
[tex]\[
(2x^3 + x^2 - 4x) - (9x^3 - 3x^2) = 2x^3 + x^2 - 4x - 9x^3 + 3x^2
\][/tex]
2. Combine Like Terms:
Now, group and combine the like terms:
- Cubic terms: [tex]\(2x^3 - 9x^3 = -7x^3\)[/tex]
- Quadratic terms: [tex]\(x^2 + 3x^2 = 4x^2\)[/tex]
- Linear terms: There is only one linear term, [tex]\(-4x\)[/tex].
3. Result:
After combining the like terms, the simplified expression is:
[tex]\[
-7x^3 + 4x^2 - 4x
\][/tex]
Thus, the correct choice is:
[tex]\[
\text{b) } -7x^3 + 4x^2 - 4x
\][/tex]
1. Distribute the Negative Sign:
The expression is given as a subtraction of two groups of terms. First, distribute the negative sign across the second set of parentheses:
[tex]\[
(2x^3 + x^2 - 4x) - (9x^3 - 3x^2) = 2x^3 + x^2 - 4x - 9x^3 + 3x^2
\][/tex]
2. Combine Like Terms:
Now, group and combine the like terms:
- Cubic terms: [tex]\(2x^3 - 9x^3 = -7x^3\)[/tex]
- Quadratic terms: [tex]\(x^2 + 3x^2 = 4x^2\)[/tex]
- Linear terms: There is only one linear term, [tex]\(-4x\)[/tex].
3. Result:
After combining the like terms, the simplified expression is:
[tex]\[
-7x^3 + 4x^2 - 4x
\][/tex]
Thus, the correct choice is:
[tex]\[
\text{b) } -7x^3 + 4x^2 - 4x
\][/tex]
