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Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], we will follow these steps:
1. Distribute the Negative Sign:
Start by distributing the negative sign across the second polynomial:
[tex]\((6x^2 - 2x - 9)\)[/tex] becomes [tex]\(-6x^2 + 2x + 9\)[/tex].
2. Combine the Polynomials:
Now, rewrite the expression by combining the polynomials with the opposite signs from the second bracket:
[tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
3. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms: There is only one term, [tex]\(5x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms: Combine [tex]\(4x^2 - 6x^2\)[/tex] which gives [tex]\(-2x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: There is only one term, [tex]\(2x\)[/tex].
- For constant terms: There is only one term, [tex]\(9\)[/tex].
After combining like terms, the simplified 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].
1. Distribute the Negative Sign:
Start by distributing the negative sign across the second polynomial:
[tex]\((6x^2 - 2x - 9)\)[/tex] becomes [tex]\(-6x^2 + 2x + 9\)[/tex].
2. Combine the Polynomials:
Now, rewrite the expression by combining the polynomials with the opposite signs from the second bracket:
[tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
3. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms: There is only one term, [tex]\(5x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms: Combine [tex]\(4x^2 - 6x^2\)[/tex] which gives [tex]\(-2x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: There is only one term, [tex]\(2x\)[/tex].
- For constant terms: There is only one term, [tex]\(9\)[/tex].
After combining like terms, the simplified 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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