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Answer :
To simplify
[tex]$$
\left(12x^3 - 8x^2\right) - \left(3x^3 + 9x^2 + x - 7\right),
$$[/tex]
follow these steps:
1. Distribute the negative sign:
The subtraction sign before the second parentheses changes the sign of every term inside:
[tex]$$
12x^3 - 8x^2 - 3x^3 - 9x^2 - x + 7.
$$[/tex]
2. Combine like terms:
- Combine the [tex]$x^3$[/tex] terms:
[tex]$$
12x^3 - 3x^3 = 9x^3.
$$[/tex]
- Combine the [tex]$x^2$[/tex] terms:
[tex]$$
-8x^2 - 9x^2 = -17x^2.
$$[/tex]
- The [tex]$x$[/tex] term is by itself:
[tex]$$
-x.
$$[/tex]
- The constant term is:
[tex]$$
+7.
$$[/tex]
3. Write the simplified expression:
Putting it all together, the simplified expression is:
[tex]$$
9x^3 - 17x^2 - x + 7.
$$[/tex]
Thus, the correct answer is:
[tex]$$
\boxed{9x^3 - 17x^2 - x + 7}.
$$[/tex]
This corresponds to option B.
[tex]$$
\left(12x^3 - 8x^2\right) - \left(3x^3 + 9x^2 + x - 7\right),
$$[/tex]
follow these steps:
1. Distribute the negative sign:
The subtraction sign before the second parentheses changes the sign of every term inside:
[tex]$$
12x^3 - 8x^2 - 3x^3 - 9x^2 - x + 7.
$$[/tex]
2. Combine like terms:
- Combine the [tex]$x^3$[/tex] terms:
[tex]$$
12x^3 - 3x^3 = 9x^3.
$$[/tex]
- Combine the [tex]$x^2$[/tex] terms:
[tex]$$
-8x^2 - 9x^2 = -17x^2.
$$[/tex]
- The [tex]$x$[/tex] term is by itself:
[tex]$$
-x.
$$[/tex]
- The constant term is:
[tex]$$
+7.
$$[/tex]
3. Write the simplified expression:
Putting it all together, the simplified expression is:
[tex]$$
9x^3 - 17x^2 - x + 7.
$$[/tex]
Thus, the correct answer is:
[tex]$$
\boxed{9x^3 - 17x^2 - x + 7}.
$$[/tex]
This corresponds to option B.
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