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]
[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]
