giannisdagoat
Answered

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What is the difference of the polynomials?

[tex]\[
(-2x^3y^2 + 4x^2y^3 - 3xy^4) - (6x^4y - 5x^2y^3 - y^5)
\][/tex]

A. [tex]\(6x^4y - 2x^3y^2 + 9x^2y^3 - 3xy^4 + y^3\)[/tex]

B. [tex]\(-6x^4y - 2x^3y^2 - x^2y^3 - 3xy^4 - y^5\)[/tex]

C. [tex]\(-6x^4y + 3x^3y^2 + 4x^2y^3 - 3xy^4 + y^3\)[/tex]

D. [tex]\(6x^4y - 7x^3y^2 + 4x^2y^3 - 3xy^4 - y^5\)[/tex]

Sagot :

GinnyAnswer
To find the difference of the two polynomials [tex]\((-2 x^3 y^2 + 4 x^2 y^3 - 3 x y^4) - (6 x^4 y - 5 x^2 y^3 - y^5)\)[/tex], we must subtract each term in the second polynomial from the corresponding terms in the first polynomial.

Given polynomials are:
[tex]\[ P_1 = -2 x^3 y^2 + 4 x^2 y^3 - 3 x y^4 \][/tex]
[tex]\[ P_2 = 6 x^4 y - 5 x^2 y^3 - y^5 \][/tex]

Now we perform the subtraction [tex]\( P_1 - P_2 \)[/tex]:

[tex]\[ (-2 x^3 y^2 + 4 x^2 y^3 - 3 x y^4) - (6 x^4 y - 5 x^2 y^3 - y^5) \][/tex]

Distribute the subtraction across the terms in [tex]\( P_2 \)[/tex]:

[tex]\[ = -2 x^3 y^2 + 4 x^2 y^3 - 3 x y^4 - 6 x^4 y + 5 x^2 y^3 + y^5 \][/tex]

Now, combine like terms:

1. There is only one [tex]\( x^4 y \)[/tex] term: [tex]\(-6 x^4 y \)[/tex].
2. There is only one [tex]\( x^3 y^2 \)[/tex] term: [tex]\( -2 x^3 y^2 \)[/tex].
3. Combine [tex]\( x^2 y^3 \)[/tex] terms: [tex]\( 4 x^2 y^3 + 5 x^2 y^3 = 9 x^2 y^3 \)[/tex].
4. There is only one [tex]\( x y^4 \)[/tex] term: [tex]\( -3 x y^4 \)[/tex].
5. There is only one [tex]\( y^5 \)[/tex] term: [tex]\( + y^5 \)[/tex].

Putting these together, we get:

[tex]\[ -6 x^4 y - 2 x^3 y^2 + 9 x^2 y^3 - 3 x y^4 + y^5 \][/tex]

So, the result is:

[tex]\[ -6 x^4 y - 2 x^3 y^2 + 9 x^2 y^3 - 3 x y^4 + y^5 \][/tex]

Among the given choices, this matches with:
[tex]\[ -6 x^4 y - 2 x^3 y^2 + 9 x^2 y^3 - 3 x y^4 + y^5 \][/tex]

Thus, the correct answer is:

[tex]\[ \boxed{-6 x^4 y-2 x^3 y^2+9 x^2 y^3-3 x y^4+y^5} \][/tex]
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