Question

What is the difference of the polynomials?

(–2x^3y^2 + 4x^2y^3 – 3xy^4) – (6x^4y – 5x^2y^3 – y^5)

A) –6x^4y – 2x^3y^2 + 9x^2y^3 – 3xy^4 + y^5
B) –6x^4y – 2x^3y^2 – x^2y^3 – 3xy^4 – y^5
C) –6x^4y + 3x^3y^2 + 4x^2y^3 – 3xy^4 + y^5
D) –6x^4y – 7x^3y^2 + 4x^2y^3 – 3xy^4 – y^5

Answer 1

The difference of the two polynomials is -6x^4y - 2x^3y^2 + 9x^2y^3 - 3xy^4 + y^5, which is found by subtracting the second polynomial from the first and combining like terms.

Step-by-step explanation:

The difference between the two polynomials is found by subtracting the second polynomial from the first. Start by distributing the negative sign through the second polynomial, then combine like terms.

(–2x^3y^2 + 4x^2y^3 – 3xy^4) – (6x^4y – 5x^2y^3 – y^5) becomes –2x^3y^2 + 4x^2y^3 – 3xy^4 – 6x^4y + 5x^2y^3 + y^5.

Next, combine like terms:

• -2x^3y^2 (no like terms)
• 4x^2y^3 + 5x^2y^3 = 9x^2y^3
• -3xy^4 (no like terms)
• -6x^4y (no like terms)
• + y^5 (no like terms)

Therefore, the difference of the polynomials is -6x^4y – 2x^3y^2 + 9x^2y^3 – 3xy^4 + y^5, which corresponds to option A.