Answer :
To simplify the given expression [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex], we need to combine like terms.
1. Identify and combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
We simply add the coefficients of [tex]\(x^3\)[/tex], which are 4 and 3, to get 7. Therefore, the combined term is [tex]\(7x^3\)[/tex].
2. Identify and combine the [tex]\(x\)[/tex] terms:
[tex]\[
-3x + 5x = 2x
\][/tex]
Here, add the coefficients of [tex]\(x\)[/tex], which are -3 and 5, to get 2. So, the combined term is [tex]\(2x\)[/tex].
3. Identify and combine the constant terms:
[tex]\[
-7 + 3 = -4
\][/tex]
For the constants, add -7 and 3 to get -4. Thus, the combined constant term is -4.
Combining all these simplified terms, the expression becomes:
[tex]\[ 7x^3 + 2x - 4 \][/tex]
Therefore, the correct simplification of the expression is [tex]\(7x^3 + 2x - 4\)[/tex]. The correct choice is:
[tex]\(7x^3 + 2x - 4\)[/tex]
1. Identify and combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
We simply add the coefficients of [tex]\(x^3\)[/tex], which are 4 and 3, to get 7. Therefore, the combined term is [tex]\(7x^3\)[/tex].
2. Identify and combine the [tex]\(x\)[/tex] terms:
[tex]\[
-3x + 5x = 2x
\][/tex]
Here, add the coefficients of [tex]\(x\)[/tex], which are -3 and 5, to get 2. So, the combined term is [tex]\(2x\)[/tex].
3. Identify and combine the constant terms:
[tex]\[
-7 + 3 = -4
\][/tex]
For the constants, add -7 and 3 to get -4. Thus, the combined constant term is -4.
Combining all these simplified terms, the expression becomes:
[tex]\[ 7x^3 + 2x - 4 \][/tex]
Therefore, the correct simplification of the expression is [tex]\(7x^3 + 2x - 4\)[/tex]. The correct choice is:
[tex]\(7x^3 + 2x - 4\)[/tex]
