Add 4a – 6b – 2c and 5a + b – 3c.

We have five steps to finish this problem right:

Write out the problem, remove the parentheses, collect like terms, add them together, and bask in our victory. Here's step one:

(4a – 6b – 2c) + (5a + b – 3c)

And two:

= 4a – 6b – 2c + 5a + b – 3c

Here's three:

= (4a + 5a) + (-6b + b) + (-2c – 3c)

Step four:

= 9a – 5b – 5c

Ahh, that does it. Step five complete.

Subtract 8x² – 2xy + 4y² from x² + 3xy – 4y².

We have to subtract the first expression from the second, so it's actually (2nd) – (1st).

(x² + 3xy – 4y²) – (8x² – 2xy + 4y²)

Remove the parentheses, and don't forget to distribute the -1. A fairy loses its wings every time someone forgets to distribute.

x² + 3xy – 4y² – 8x² + 2xy – 4y²

Collect all the like terms.

(x² – 8x²) + (3xy + 2xy) + (-4y² – 4y²) =

-7x² + 5xy – 8y²

Add 2a²b – 7ab – 3ab² and a²b + 5ab – 7ab².

Numbers go up, numbers go down. You can't explain that—except with math.

(2a²b – 7ab – 3ab²) + (a²b + 5ab – 7ab²)

Dump the parentheses and get ready to add.

2a²b – 7ab – 3ab² + a²b + 5ab – 7ab²

Just vacuum up the like terms. That'll sort them out.

(2a²b + a²b) + (-7ab + 5ab) + (-3ab² – 7ab²) =

3a²b – 2ab – 10ab²

Simplify 2e – [2d – (5e – c + 3d)] – [6c + 3e – (4d – e)].

Grab the vacuum again. We have a mess to clean up. Let's start by dropping those parentheses and distributing the negatives.

2e – [2d – 5e + c – 3d] – [6c + 3e – 4d + e] =

2e – 2d + 5e – c + 3d – 6c – 3e + 4d – e

We take our time when removing parentheses from an expression. It's too easy to make a mistake otherwise. Now group those like terms together and finish up.

(2e + 5e – 3e – e) + (-2d + 3d + 4d) + (-c – 6c) =

3e + 5d – 7c