Answer :
To solve the problem of subtracting [tex]\((3x^4 + 2x^2 - 6)\)[/tex] from [tex]\((4x^4 + 2x^2 - 6)\)[/tex], we follow these steps:
1. Write Down the Expressions:
- The first polynomial is [tex]\((4x^4 + 2x^2 - 6)\)[/tex].
- The second polynomial is [tex]\((3x^4 + 2x^2 - 6)\)[/tex].
2. Set Up the Subtraction:
- We want to subtract the second polynomial from the first polynomial:
[tex]\(\left(4x^4 + 2x^2 - 6\right) - \left(3x^4 + 2x^2 - 6\right)\)[/tex].
3. Apply the Subtraction:
- Distribute the subtraction sign through the second polynomial:
[tex]\[4x^4 + 2x^2 - 6 - 3x^4 - 2x^2 + 6.\][/tex]
4. Combine Like Terms:
- Combine terms involving [tex]\(x^4\)[/tex]: [tex]\(4x^4 - 3x^4 = x^4\)[/tex].
- Combine terms involving [tex]\(x^2\)[/tex]: [tex]\(2x^2 - 2x^2 = 0\)[/tex].
- Combine constant terms: [tex]\(-6 + 6 = 0\)[/tex].
5. Write the Result:
- The simplified result after combining like terms is [tex]\(x^4\)[/tex].
Therefore, the result of [tex]\((3x^4 + 2x^2 - 6)\)[/tex] subtracted from [tex]\((4x^4 + 2x^2 - 6)\)[/tex] is [tex]\(x^4\)[/tex].
1. Write Down the Expressions:
- The first polynomial is [tex]\((4x^4 + 2x^2 - 6)\)[/tex].
- The second polynomial is [tex]\((3x^4 + 2x^2 - 6)\)[/tex].
2. Set Up the Subtraction:
- We want to subtract the second polynomial from the first polynomial:
[tex]\(\left(4x^4 + 2x^2 - 6\right) - \left(3x^4 + 2x^2 - 6\right)\)[/tex].
3. Apply the Subtraction:
- Distribute the subtraction sign through the second polynomial:
[tex]\[4x^4 + 2x^2 - 6 - 3x^4 - 2x^2 + 6.\][/tex]
4. Combine Like Terms:
- Combine terms involving [tex]\(x^4\)[/tex]: [tex]\(4x^4 - 3x^4 = x^4\)[/tex].
- Combine terms involving [tex]\(x^2\)[/tex]: [tex]\(2x^2 - 2x^2 = 0\)[/tex].
- Combine constant terms: [tex]\(-6 + 6 = 0\)[/tex].
5. Write the Result:
- The simplified result after combining like terms is [tex]\(x^4\)[/tex].
Therefore, the result of [tex]\((3x^4 + 2x^2 - 6)\)[/tex] subtracted from [tex]\((4x^4 + 2x^2 - 6)\)[/tex] is [tex]\(x^4\)[/tex].
