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Answer :
To simplify the expression
[tex]$$
\left(6x^4 + 7x + 5x^3\right) - \left(4x^4 - 2x^3 + 3x\right),
$$[/tex]
follow these steps:
1. Remove Parentheses:
Distribute the subtraction sign (i.e., change the sign of every term in the second group):
[tex]$$
6x^4 + 7x + 5x^3 - 4x^4 + 2x^3 - 3x.
$$[/tex]
2. Combine Like Terms:
Group and combine the terms with the same exponent.
- For the [tex]$x^4$[/tex] terms:
[tex]$$
6x^4 - 4x^4 = 2x^4.
$$[/tex]
- For the [tex]$x^3$[/tex] terms:
[tex]$$
5x^3 + 2x^3 = 7x^3.
$$[/tex]
- For the [tex]$x$[/tex] terms:
[tex]$$
7x - 3x = 4x.
$$[/tex]
3. Write the Simplified Expression:
Putting the combined results together, we obtain:
[tex]$$
2x^4 + 7x^3 + 4x.
$$[/tex]
Thus, the simplified expression is
[tex]$$
\boxed{2x^4 + 7x^3 + 4x}.
$$[/tex]
Among the provided answer choices, this corresponds to option B.
[tex]$$
\left(6x^4 + 7x + 5x^3\right) - \left(4x^4 - 2x^3 + 3x\right),
$$[/tex]
follow these steps:
1. Remove Parentheses:
Distribute the subtraction sign (i.e., change the sign of every term in the second group):
[tex]$$
6x^4 + 7x + 5x^3 - 4x^4 + 2x^3 - 3x.
$$[/tex]
2. Combine Like Terms:
Group and combine the terms with the same exponent.
- For the [tex]$x^4$[/tex] terms:
[tex]$$
6x^4 - 4x^4 = 2x^4.
$$[/tex]
- For the [tex]$x^3$[/tex] terms:
[tex]$$
5x^3 + 2x^3 = 7x^3.
$$[/tex]
- For the [tex]$x$[/tex] terms:
[tex]$$
7x - 3x = 4x.
$$[/tex]
3. Write the Simplified Expression:
Putting the combined results together, we obtain:
[tex]$$
2x^4 + 7x^3 + 4x.
$$[/tex]
Thus, the simplified expression is
[tex]$$
\boxed{2x^4 + 7x^3 + 4x}.
$$[/tex]
Among the provided answer choices, this corresponds to option B.
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