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Answer :
Sure! Let's find the difference of the given polynomials step by step.
We are given the expression:
[tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex].
To solve this, we need to subtract the second polynomial from the first. We do this by distributing the negative sign to each term in the second polynomial and then combining like terms. Here’s how it works:
1. Distribute the negative sign:
- [tex]\(-(6x^2 - 2x - 9)\)[/tex] becomes [tex]\(-6x^2 + 2x + 9\)[/tex].
2. Rewrite the expression:
- Now our expression looks like this: [tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
3. Combine like terms:
- Start with the [tex]\(x^3\)[/tex] terms: we only have [tex]\(5x^3\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] term is just [tex]\(2x\)[/tex].
- Finally, the constant term is [tex]\(9\)[/tex].
Putting it all together, the combined expression is:
[tex]\[5x^3 - 2x^2 + 2x + 9\][/tex]
So, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
We are given the expression:
[tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex].
To solve this, we need to subtract the second polynomial from the first. We do this by distributing the negative sign to each term in the second polynomial and then combining like terms. Here’s how it works:
1. Distribute the negative sign:
- [tex]\(-(6x^2 - 2x - 9)\)[/tex] becomes [tex]\(-6x^2 + 2x + 9\)[/tex].
2. Rewrite the expression:
- Now our expression looks like this: [tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
3. Combine like terms:
- Start with the [tex]\(x^3\)[/tex] terms: we only have [tex]\(5x^3\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] term is just [tex]\(2x\)[/tex].
- Finally, the constant term is [tex]\(9\)[/tex].
Putting it all together, the combined expression is:
[tex]\[5x^3 - 2x^2 + 2x + 9\][/tex]
So, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
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