High School

Simplify [tex]\left(6x^2 - 3 - 5x^3\right) - \left(4x^3 + 2x^2 - 8\right)[/tex].

A. [tex]9x^3 - 4x^2 - 5[/tex]
B. [tex]-9x^3 + 4x^2 + 5[/tex]
C. [tex]x^3 - x^2 - 13x^3[/tex]
D. [tex]-x^3 + x^2 + 13x^3[/tex]

Answer :

We start with the expression

[tex]$$
\left(6x^2 - 3 - 5x^3\right) - \left(4x^3 + 2x^2 - 8\right).
$$[/tex]

First, we remove the parentheses by distributing the subtraction:

[tex]$$
6x^2 - 3 - 5x^3 - 4x^3 - 2x^2 + 8.
$$[/tex]

Next, we group like terms. Group the [tex]$x^3$[/tex], [tex]$x^2$[/tex], and constant terms:

- The [tex]$x^3$[/tex] terms: [tex]$-5x^3 - 4x^3 = -9x^3$[/tex].
- The [tex]$x^2$[/tex] terms: [tex]$6x^2 - 2x^2 = 4x^2$[/tex].
- The constants: [tex]$-3 + 8 = 5$[/tex].

Thus, after combining the like terms, we obtain

[tex]$$
-9x^3 + 4x^2 + 5.
$$[/tex]

So, the simplified expression is

[tex]$$
-9x^3 + 4x^2 + 5.
$$[/tex]