Answer :
We are given the expression
[tex]$$\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right).$$[/tex]
Step 1: Remove the Parentheses
Distribute the minus sign across the second polynomial:
[tex]$$
5x^3 + 4x^2 - 6x^2 + 2x + 9.
$$[/tex]
Step 2: Combine Like Terms
Group the like terms together:
- The [tex]$x^3$[/tex] term remains: [tex]$$5x^3.$$[/tex]
- Combine the [tex]$x^2$[/tex] terms: [tex]$$4x^2 - 6x^2 = -2x^2.$$[/tex]
- The [tex]$x$[/tex] term is: [tex]$$+ 2x.$$[/tex]
- The constant term is: [tex]$$+ 9.$$[/tex]
So, the simplified expression becomes:
[tex]$$
5x^3 - 2x^2 + 2x + 9.
$$[/tex]
Final Answer
The difference of the polynomials is
[tex]$$\boxed{5x^3 - 2x^2 + 2x + 9}.$$[/tex]
[tex]$$\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right).$$[/tex]
Step 1: Remove the Parentheses
Distribute the minus sign across the second polynomial:
[tex]$$
5x^3 + 4x^2 - 6x^2 + 2x + 9.
$$[/tex]
Step 2: Combine Like Terms
Group the like terms together:
- The [tex]$x^3$[/tex] term remains: [tex]$$5x^3.$$[/tex]
- Combine the [tex]$x^2$[/tex] terms: [tex]$$4x^2 - 6x^2 = -2x^2.$$[/tex]
- The [tex]$x$[/tex] term is: [tex]$$+ 2x.$$[/tex]
- The constant term is: [tex]$$+ 9.$$[/tex]
So, the simplified expression becomes:
[tex]$$
5x^3 - 2x^2 + 2x + 9.
$$[/tex]
Final Answer
The difference of the polynomials is
[tex]$$\boxed{5x^3 - 2x^2 + 2x + 9}.$$[/tex]
