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Answer :
Let's simplify the expression [tex]\((2x^2 + 7x^3 - 5x^4) - (4x^4 + 2x^2 - 5x^3)\)[/tex].
1. Distribute the Negative Sign:
When you have a subtraction of polynomials, you need to distribute the negative sign across the second polynomial. This means you'll change the sign of each term in the second polynomial:
[tex]\((2x^2 + 7x^3 - 5x^4) - (4x^4 + 2x^2 - 5x^3)\)[/tex]
becomes
[tex]\(2x^2 + 7x^3 - 5x^4 - 4x^4 - 2x^2 + 5x^3\)[/tex].
2. Combine Like Terms:
Now, combine the like terms in the expression:
- For [tex]\(x^2\)[/tex] terms:
[tex]\(2x^2 - 2x^2 = 0\)[/tex].
- For [tex]\(x^3\)[/tex] terms:
[tex]\(7x^3 + 5x^3 = 12x^3\)[/tex].
- For [tex]\(x^4\)[/tex] terms:
[tex]\(-5x^4 - 4x^4 = -9x^4\)[/tex].
3. Write the Simplified Expression:
The expression simplifies to [tex]\(-9x^4 + 12x^3\)[/tex].
Therefore, the correct simplified form of the expression is [tex]\(-9x^4 + 12x^3\)[/tex], which matches with the option [tex]\(-9x^4 + 12x^3\)[/tex].
1. Distribute the Negative Sign:
When you have a subtraction of polynomials, you need to distribute the negative sign across the second polynomial. This means you'll change the sign of each term in the second polynomial:
[tex]\((2x^2 + 7x^3 - 5x^4) - (4x^4 + 2x^2 - 5x^3)\)[/tex]
becomes
[tex]\(2x^2 + 7x^3 - 5x^4 - 4x^4 - 2x^2 + 5x^3\)[/tex].
2. Combine Like Terms:
Now, combine the like terms in the expression:
- For [tex]\(x^2\)[/tex] terms:
[tex]\(2x^2 - 2x^2 = 0\)[/tex].
- For [tex]\(x^3\)[/tex] terms:
[tex]\(7x^3 + 5x^3 = 12x^3\)[/tex].
- For [tex]\(x^4\)[/tex] terms:
[tex]\(-5x^4 - 4x^4 = -9x^4\)[/tex].
3. Write the Simplified Expression:
The expression simplifies to [tex]\(-9x^4 + 12x^3\)[/tex].
Therefore, the correct simplified form of the expression is [tex]\(-9x^4 + 12x^3\)[/tex], which matches with the option [tex]\(-9x^4 + 12x^3\)[/tex].
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