High School

Simplify [tex]\left(12 x^3-8 x^2\right)-\left(3 x^3+9 x^2+x-7\right)[/tex].

A. [tex]9 x^3+x^2-x+7[/tex]
B. [tex]9 x^3-17 x^2-x+7[/tex]
C. [tex]15 x^3-17 x^2-x-7[/tex]
D. [tex]15 x^3+x^2+x-7[/tex]

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.