\(\displaystyle 14x - 5 (x + 8)\)

\(\displaystyle = 14x - 5 \cdot x - 5 \cdot 8\)

\(\displaystyle = 14x - 5x - 40\)

\(\displaystyle = (14- 5) x - 40\)

\(\displaystyle = 9x - 40\)

\(\displaystyle 8 (x - 7) - 3(x + 2)\)

\(\displaystyle = 8 \cdot x -8 \cdot 7 - 3 \cdot x + (-3) \cdot 2\)

\(\displaystyle = 8x -56 - 3 x -6\)

\(\displaystyle = 8x - 3 x -56 -6\)

\(\displaystyle =( 8 - 3 ) x - (56 + 6)\)

\(\displaystyle =5 x - 62\)

This problem is just a matter of grouping together like terms.  Remember that terms like \(\displaystyle xy\) are treated as though they were their own, different variable:

\(\displaystyle 3x + 4x - 3y - 15y + 2xy\)

The only part that might be a little hard is:

\(\displaystyle -3y - 15y\)

If you are confused, think of your number line.  This is like "going back" (more negative) from 15.  Therefore, you ranswer will be:

\(\displaystyle 7x + 2xy - 18y\)

This problem really is a trick question.  There are no common terms among any of the parts of the expression to be simplified.  In each case, you have an independent variable or set of variables: \(\displaystyle x, y, xy,\) and \(\displaystyle yz\).  Therefore, do not combine any of the elements!

Remember, when there is a subtraction outside of a group, you should add the opposite of each member.  That is:

\(\displaystyle 5x + 3y - (4x + 2y) = 5x + 3y + (-4x) + (-2y)\)

That is a bit confusing, so let's simplify.  When you add a negative, you subtract:

\(\displaystyle 5x + 3y - 4x - 2y\)

Now, group your like variables:

\(\displaystyle 5x- 4x + 3y - 2y\)

Finally, perform the subtractions and get: \(\displaystyle x + y\)

Begin by rewriting the subtracted group as a set of added negative numbers:

\(\displaystyle 4xy + 3y - (2xy + 3x) - y = 4xy + 3y + (-2xy) + (-3x) - y\)

Now, simplify that a little by rewriting the additions of negatives as being mere subtractions:

\(\displaystyle 4xy + 3y - 2xy - 3x - y\)

Next, move the like terms next to each other:

\(\displaystyle 4xy - 2xy + 3y- y - 3x\)

Finally, combine like terms:

\(\displaystyle 2xy + 2y - 3x\)

You need to begin by distributing the minus sign through the whole group \(\displaystyle (13b - 2a)\).  This gives you:

\(\displaystyle 15a + 23b - (13b - 2a) = 15a + 23b - 13b - (-2a)\)

Simplifying the double negative, you get:

\(\displaystyle 15a + 23b - 13b + 2a\)

Now, you can move the like terms next to each other:

\(\displaystyle 15a + 2a + 23b - 13b\)

Finally, simplify:

\(\displaystyle 17a + 10b\)

This problem is as simple as it appears.  All that you need to do is group together like terms:

\(\displaystyle 4x - 3x + 3y - 3z + 2\)

The only like terms are the \(\displaystyle x\) terms.  Therefore, the simple answer is a matter of subtracting 3 from 4:

\(\displaystyle x + 3y - 3z + 2\)

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:

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