Question

(4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y)

Place the correct coefficients in the difference.

x2y3 +
xy2 +
y

Answer 1

the coefficients of x^2y^3, xy^2, and y in the difference are 11, 8, and -4, respectively.

Explanation:

To subtract the second polynomial from the first, we need to change the sign of each term in the second polynomial. This gives us:

(4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 - 6xy^2 + 2y)

Simplifying the double negative in the second polynomial, we get:

(4x^2y^3 + 2xy^2 - 2y) + 7x^2y^3 + 6xy^2 - 2y

Now we can combine like terms. The terms with x^2y^3 are 4x^2y^3 + 7x^2y^3 = 11x^2y^3. The terms with xy^2 are 2xy^2 + 6xy^2 = 8xy^2. The terms with y are -2y - 2y = -4y. Putting it all together, we get:

11x^2y^3 + 8xy^2 - 4y

Therefore, the coefficients of x^2y^3, xy^2, and y in the difference are 11, 8, and -4, respectively.