Post 4: Are You Ready? Simplifying Expressions

(by Mark O. with help from Sage the intrepid student dog)

As Sage enters the door, he finds himself in a narrow hallway. The walls, floor, and ceiling are all covered with equations. However, these equations seem different than the ones he's been seeing. They seem somehow more solid. And they're multiplying. There are so many letters and numbers that they're actually starting to come out of the walls and are starting to fill the room!

Sage is getting worried. The group of kids seems worried too. They get stressed out when equations get cluttered with a bunch of numbers and letters. To help them calm down, it's good to try to reduce the number of numbers and letters in your equations as much as possible.

We're going to look at three common ways that people miss opportunities to clean up and simplify their equations:

Problem 1: Forgetting to combine like terms

A lot of times, you might have a bunch of terms that might make your equations too crowded, so put them together to simplify them!

Which of these two equations can be simplified (combined) further?

A) x² + 3x + 10 = 7 B) x² + 2x + x + 10 = 7

(It's B)

Let's take a look at some ways that we can continue to simplify equations:

Problem 2: Distributing across parentheses

Parentheses are a place where it is easy to make mistakes. Take a look below for some tips on managing parentheses.

Which one of these looks correct?

A) 3(x + 4) = 3x+4 B) 3(x + 4) = 3x + 12

(It's B.)

Problem 3: Not simplifying with exponents

Exponents scare Sage a little. They sometimes have trouble remembering all the rules and are afraid that they might make a mistake. But exponents don't need to be that scary when we remember the ways that we can make them simpler!

Which of these looks right?

A) x⁶/x³ = x³ B) x⁶/x³=x²

(It's A)

Let's take a look at some ways to handle simplifying exponents:

Phew! As Sage starts to simplify all the equations in the room, the room clears. Sage feels like she has a bit more room to think now, and he sees the end of the tunnel. As you walk through the door, Sage things about how important it is to remember that you can clean up your equations, and make it easier for you to think and to solve! Sage is shocked to see a man is already in the next room...

Catch your algebra mistakes before they cost you

The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.

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