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Answer :
Sure! Let's simplify the expression [tex]\((6x^4 + 7x + 5x^3) - (4x^4 - 2x^3 + 3x)\)[/tex] step-by-step.
1. Distribute the negative sign: When you have a subtraction like this, it's helpful to distribute the negative sign to each term in the second set of parentheses. So, the expression becomes:
[tex]\[
6x^4 + 7x + 5x^3 - 4x^4 + 2x^3 - 3x
\][/tex]
2. Combine like terms: Now, let's group and combine the terms that have the same power of [tex]\(x\)[/tex].
- 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: After combining like terms, the simplified expression is:
[tex]\[
2x^4 + 7x^3 + 4x
\][/tex]
So, the correct simplified expression is [tex]\(2x^4 + 7x^3 + 4x\)[/tex], which matches option B.
1. Distribute the negative sign: When you have a subtraction like this, it's helpful to distribute the negative sign to each term in the second set of parentheses. So, the expression becomes:
[tex]\[
6x^4 + 7x + 5x^3 - 4x^4 + 2x^3 - 3x
\][/tex]
2. Combine like terms: Now, let's group and combine the terms that have the same power of [tex]\(x\)[/tex].
- 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: After combining like terms, the simplified expression is:
[tex]\[
2x^4 + 7x^3 + 4x
\][/tex]
So, the correct simplified expression is [tex]\(2x^4 + 7x^3 + 4x\)[/tex], which matches option B.
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