Answer :
To simplify
[tex]$$\left(4x^3 - 3x - 7\right) + \left(3x^3 + 5x + 3\right),$$[/tex]
follow these steps:
1. Combine the cubic terms ([tex]$x^3$[/tex]):
The cubic term in the first polynomial is [tex]$4x^3$[/tex] and in the second is [tex]$3x^3$[/tex]. Adding these gives:
[tex]$$4x^3 + 3x^3 = 7x^3.$$[/tex]
2. Combine the linear terms ([tex]$x$[/tex]):
The linear term in the first polynomial is [tex]$-3x$[/tex] and in the second is [tex]$5x$[/tex]. Adding these gives:
[tex]$$-3x + 5x = 2x.$$[/tex]
3. Combine the constant terms:
The constant in the first polynomial is [tex]$-7$[/tex] and in the second is [tex]$3$[/tex]. Adding these gives:
[tex]$$-7 + 3 = -4.$$[/tex]
4. Write the final simplified polynomial:
Putting it all together, we obtain:
[tex]$$7x^3 + 2x - 4.$$[/tex]
Thus, the correct simplification is
[tex]$$\boxed{7x^3 + 2x - 4}.$$[/tex]
[tex]$$\left(4x^3 - 3x - 7\right) + \left(3x^3 + 5x + 3\right),$$[/tex]
follow these steps:
1. Combine the cubic terms ([tex]$x^3$[/tex]):
The cubic term in the first polynomial is [tex]$4x^3$[/tex] and in the second is [tex]$3x^3$[/tex]. Adding these gives:
[tex]$$4x^3 + 3x^3 = 7x^3.$$[/tex]
2. Combine the linear terms ([tex]$x$[/tex]):
The linear term in the first polynomial is [tex]$-3x$[/tex] and in the second is [tex]$5x$[/tex]. Adding these gives:
[tex]$$-3x + 5x = 2x.$$[/tex]
3. Combine the constant terms:
The constant in the first polynomial is [tex]$-7$[/tex] and in the second is [tex]$3$[/tex]. Adding these gives:
[tex]$$-7 + 3 = -4.$$[/tex]
4. Write the final simplified polynomial:
Putting it all together, we obtain:
[tex]$$7x^3 + 2x - 4.$$[/tex]
Thus, the correct simplification is
[tex]$$\boxed{7x^3 + 2x - 4}.$$[/tex]
