First, start by distributing the subtraction through the terms in parentheses.  Note that you will be subtracting negative numbers:

$\displaystyle 21x + 51xy - 3x - 2x - (-15xy)$

Subtracting a negative is the same as adding a positive:

$\displaystyle 21x + 51xy - 3x - 2x +15xy$

Now, group the like terms:

$\displaystyle 21x - 3x - 2x+ 51xy +15xy$

All you need to do now is combine like terms:

$\displaystyle 16x + 66xy$

Begin by distributing the subtraction through the parentheses:

$\displaystyle 33x + 25y - 22xy + 2z - 22y - 21x - 4z$

Next, group the like terms:

$\displaystyle 33x - 21x + 25y - 22y - 22xy + 2z - 4z$

Now, combine them:

$\displaystyle 12x + 3y - 22xy -2z$

Begin by putting similar variables together.  Remember that combinations of variables such as $\displaystyle x^2y$ are treated like a separate variable:

$\displaystyle 31x + 21y - 2y + 3x^{2} - 2x^{2} + 2x^{2}y$

Combine like terms:

$\displaystyle 31x + 19y + x^{2} + 2x^{2}y$

You can then rearrange the variables to get the answer as written:

$\displaystyle 31x + x^{2} + 19y + 2x^{2}y$

Begin by distributing the $\displaystyle -3$:

$\displaystyle 57x - 3(4x) - (-3)(5y)$

Multiply each factor:

$\displaystyle 57x - 12x - (-15y)$

Change the double negation to addition:

$\displaystyle 57x - 12x +15y$

Combine like terms:

$\displaystyle 45x + 15y$

Begin by distributing the $\displaystyle -2$:

$\displaystyle 55x - 13xy + (-2)5y + (-2)10xy$

Multiply all factors:

$\displaystyle 55x - 13xy + (-10)y + (-20)xy$

Group together the only like factor ($\displaystyle xy$):

$\displaystyle 55x - 13xy-20xy -10y$

Combine like terms:

$\displaystyle 55x - 33xy -10y$

Begin by moving all like terms next to each other.  Remember that you must treat every variable type separately:

$\displaystyle 5xy - 14xy + 21x - 3y + 2x^{2}$

Combine like terms:

$\displaystyle -9xy + 21x - 3y + 2x^{2}$

You merely need to reorder the variables to get to the form in the answer choice.

Begin by distributing the $\displaystyle 4$ through the group:

$\displaystyle 3x + 14y + 4(xy) - (4)(4x)$

Next, perform the multiplications:

$\displaystyle 3x + 14y + 4xy - 16x$

Group the like terms:

$\displaystyle 3x - 16x+ 14y + 4xy$

Combine like terms:

$\displaystyle -13x+ 14y + 4xy$

Rearrange the terms to get the answer as it appears in the answer choices.

Begin by multiplying through by $\displaystyle -4$:

$\displaystyle 43x^{2} + 2xy - 3y + (-4)(7xy) - (-4)(22x^{2})$

Perform the multiplications:

$\displaystyle 43x^{2} + 2xy - 3y - 28xy - (-88x^{2})$

The double negation becomes addition:

$\displaystyle 43x^{2} + 2xy - 3y - 28xy + 88x^{2}$

Group like terms:

$\displaystyle 43x^{2}+ 88x^{2} + 2xy - 28xy - 3y$

Combine like terms:

$\displaystyle 131x^{2} + 26xy - 3y$

$\displaystyle 8(x+7) - 3 (x + 10)$

$\displaystyle = 8 \cdot x+ 8 \cdot 7 - 3 \cdot x - 3 \cdot 10$

$\displaystyle = 8 x+ 56 - 3x - 30$

$\displaystyle = 5x+ 26$

$\displaystyle 5-9 = 5 + (-9)= -(9-5) = -4$ in normal arithmetic.

In modulo 11 arithmetic, a negative number has 11 added to it as many times as necessary until a positive sum is reached:

$\displaystyle -4 + 11 = 7$

Therefore, 

$\displaystyle 5-9 \equiv 7 \mod 11$