Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], let's go through the steps:
1. Rewrite the expression without parentheses:
[tex]\[
5x^3 + 4x^2 - (6x^2 - 2x - 9)
\][/tex]
2. Distribute the negative sign to the second polynomial:
- When subtracting a polynomial, change the sign of each term inside the parentheses.
- This becomes:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine like terms:
- For [tex]\(x^3\)[/tex], there's only one term: [tex]\(5x^3\)[/tex].
- For [tex]\(x^2\)[/tex], combine [tex]\(4x^2\)[/tex] and [tex]\(-6x^2\)[/tex], which results in:
[tex]\[
4x^2 - 6x^2 = -2x^2
\][/tex]
- For [tex]\(x\)[/tex], there's only one term: [tex]\(2x\)[/tex].
- For the constant term, it's [tex]\(+9\)[/tex].
4. Write the simplified expression:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Thus, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Rewrite the expression without parentheses:
[tex]\[
5x^3 + 4x^2 - (6x^2 - 2x - 9)
\][/tex]
2. Distribute the negative sign to the second polynomial:
- When subtracting a polynomial, change the sign of each term inside the parentheses.
- This becomes:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine like terms:
- For [tex]\(x^3\)[/tex], there's only one term: [tex]\(5x^3\)[/tex].
- For [tex]\(x^2\)[/tex], combine [tex]\(4x^2\)[/tex] and [tex]\(-6x^2\)[/tex], which results in:
[tex]\[
4x^2 - 6x^2 = -2x^2
\][/tex]
- For [tex]\(x\)[/tex], there's only one term: [tex]\(2x\)[/tex].
- For the constant term, it's [tex]\(+9\)[/tex].
4. Write the simplified expression:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Thus, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
