What is the difference of the polynomials?
(-2x3y² + 4x²³-3xy) – (6xy – 5×23-
-6xy-2x3y²+9x2y³-3xy + y
-6x²-2x3y²- 2 – 3×4 – 5
-6x²y + 3x3y² + 4x2y² – 3xy + y5
-6xy-7x3y²+4x²y³-3xy-y5
The Correct Answer and Explanation is:
To find the difference of the polynomials, we need to subtract one polynomial from another. Let’s break down the process step-by-step.
The problem is:
[
(-2x^3y^2 + 4x^2y^3 – 3xy) – (6xy – 5x^2y^3 – 6xy – 2x^3y^2 + 9x^2y^3 – 3xy + y – 6x^2 – 2x^3y^2 – 2 – 3x^4 – 5 – 6x^2y + 3x^3y^2 + 4x^2y^3 – 3xy + y^5 – 6xy – 7x^3y^2 + 4x^2y^3 – 3xy – y^5)
]
Step 1: Group similar terms
We can organize this expression by grouping like terms (terms that have the same variable powers).
First Polynomial:
[
-2x^3y^2 + 4x^2y^3 – 3xy
]
Second Polynomial:
[
6xy – 5x^2y^3 – 6xy – 2x^3y^2 + 9x^2y^3 – 3xy + y – 6x^2 – 2x^3y^2 – 2 – 3x^4 – 5 – 6x^2y + 3x^3y^2 + 4x^2y^3 – 3xy + y^5 – 6xy – 7x^3y^2 + 4x^2y^3 – 3xy – y^5
]
Step 2: Subtract the terms
We now subtract the terms of the second polynomial from the first, making sure to distribute the negative sign to each term of the second polynomial.
- x^3y^2 terms:
[
-2x^3y^2 – (-2x^3y^2 – 2x^3y^2 – 7x^3y^2 + 3x^3y^2) = -2x^3y^2 + 2x^3y^2 + 2x^3y^2 + 7x^3y^2 – 3x^3y^2 = -5x^3y^2
] - x^2y^3 terms:
[
4x^2y^3 – (9x^2y^3 – 5x^2y^3 + 4x^2y^3 + 4x^2y^3) = 4x^2y^3 – 9x^2y^3 + 5x^2y^3 – 4x^2y^3 – 4x^2y^3 = -4x^2y^3
] - xy terms:
[
-3xy – (6xy + 6xy + 3xy + 3xy + 6xy) = -3xy – 6xy – 6xy – 3xy – 3xy – 6xy = -27xy
] - Constant terms:
[
y – 2 – 5 – 2 = y – 9
] - x^2 terms:
[
-6x^2 = -6x^2
] - x^4 terms:
[
-3x^4
] - y^5 terms:
[
-y^5
] - x^2y terms:
[
-6x^2y
]
Step 3: Combine the results
Now, combine all the terms:
[
-5x^3y^2 – 4x^2y^3 – 27xy + y – 9 – 6x^2 – 3x^4 – y^5 – 6x^2y
]
Final Answer:
The difference of the polynomials is:
[
-5x^3y^2 – 4x^2y^3 – 27xy + y – 9 – 6x^2 – 3x^4 – y^5 – 6x^2y
]
Explanation:
The key to subtracting polynomials is aligning like terms with the same variable powers. When subtracting polynomials, distribute the negative sign across all terms of the second polynomial. After combining the like terms, we obtain the simplified result.
This process ensures that every term is handled carefully, and we ensure the proper operation is applied to each term during the subtraction.