Answer:

Step-by-step explanation:

A) 4x²- 5xy + 3y² and -6x² - 4xy + 2y²:

Begin by adding the coefficients of the x² terms: 4x² and -6x².

The result is -2x².

Next, add the coefficients of the y² terms: 3y² and 2y².

The result is 5y².

Finally, add the coefficients of the xy terms: -5xy and -4xy.

The result is -9xy.

The sum of these two expressions is -2x² - 9xy + 5y².

B) 3a - 4b, 5a + 2b and -7a -3b:

Begin by adding the coefficients of the a terms: 3a, 5a and -7a.

The result is 1a.

Next, add the coefficients of the b terms: -4b and 2b.

The result is -2b.

The sum of these three expressions is 1a - 2b.

C) x³ - 2x²y-y³ , 7x²y - 4x³ and 4y³+5x²y:

Begin by adding the coefficients of the x³ terms: -4x³ and x³.

The result is -3x³.

Next, add the coefficients of the x²y terms: -2x²y and 7x²y.

The result is 5x²y.

Finally, add the coefficients of the y³ terms: -y³ and 4y³.

The result is 3y³.

The sum of these three expressions is -3x³ + 5x²y + 3y³.

D) 6m²n + 3mn - 2n² , n² - nm - m²n and mn - 3n² - 5m²n:

Begin by adding the coefficients of the m²n terms: 6m²n, -m²n and -5m²n.

The result is -2m²n.

Next, add the coefficients of the mn terms: 3mn, -mn and -mn.

The result is -6mn.

Finally, add the coefficients of the n² terms: -2n², -n² and -3n².

The result is -6n².

The sum of these three expressions is -2m²n - 6mn - 6n².