Gibson Floyd
04/08/2024 · Junior High School
Which polynomial correctly combines the like terms and expresses the given polynomial in standard \( f \) \( \begin{array}{l}9 x y^{3}-4 y^{4}-10 x^{2} y^{2}+x^{3} y+3 x^{4}+2 x^{2} y^{2}-9 y^{4} \\ -13 y^{4}+3 x^{4}-8 x^{2} y^{2}+x^{3} y+9 x y^{3} \\ -13 y^{4}+x^{3} y-8 x^{2} y^{2}+9 x y^{3}+3 x^{4} \\ 3 x^{4}-8 x^{2} y^{2}+x^{3} y+9 x y^{3}-13 y^{4} \\ 3 x^{4}+x^{3} y-8 x^{2} y^{2}+9 x y^{3}-13 y^{4}\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To combine the like terms and express the given polynomial in standard form, we will first write down the polynomial clearly and then group the like terms.
The given polynomial is:
\[
9xy^3 - 4y^4 - 10x^2y^2 + x^3y + 3x^4 + 2x^2y^2 - 9y^4 - 13y^4 + 3x^4 - 8x^2y^2 + x^3y + 9xy^3 - 13y^4 + x^3y - 8x^2y^2 + 9xy^3 + 3x^4 - 8x^2y^2 + x^3y + 9xy^3 - 13y^4 + 3x^4 + x^3y - 8x^2y^2 + 9xy^3 - 13y^4
\]
Now, let's combine the like terms:
1. **Terms with \(x^4\)**:
- \(3x^4 + 3x^4 + 3x^4 + 3x^4 = 12x^4\)
2. **Terms with \(x^3y\)**:
- \(x^3y + x^3y + x^3y + x^3y + x^3y = 5x^3y\)
3. **Terms with \(x^2y^2\)**:
- \(-10x^2y^2 + 2x^2y^2 - 8x^2y^2 - 8x^2y^2 - 8x^2y^2 = -32x^2y^2\)
4. **Terms with \(xy^3\)**:
- \(9xy^3 + 9xy^3 + 9xy^3 + 9xy^3 + 9xy^3 = 45xy^3\)
5. **Terms with \(y^4\)**:
- \(-4y^4 - 9y^4 - 13y^4 - 13y^4 - 13y^4 = -52y^4\)
Now, we can write the polynomial in standard form, which is typically ordered by the degree of the terms:
\[
f(x, y) = 12x^4 + 5x^3y - 32x^2y^2 + 45xy^3 - 52y^4
\]
Thus, the polynomial that correctly combines the like terms and expresses the given polynomial in standard form is:
\[
\boxed{12x^4 + 5x^3y - 32x^2y^2 + 45xy^3 - 52y^4}
\]
Quick Answer
The polynomial in standard form is \( 12x^4 + 5x^3y - 32x^2y^2 + 45xy^3 - 52y^4 \).
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