Question

The 5 Most Common Math Mistakes I See on QC

Answer 1

1. Trying to combine unlike terms.

You cannot combine 5x + 3 to get 8x or 8y because 5x and 3 are not like terms. In order to be like terms they must have the exact same variables raised to the exact same power. If you end up with something like 5x + 3 as your answer you must leave it like that ~unless~ you are given a value of x.

According to this logic yx^2 and xy^2 are not like terms but yx^2 and (x^2)y are.

Answer 2

2. PEMDAS

This acronym is kind of misleading. It implies that multiplication ~always~ comes before division and addition ~always~ comes before subtraction. However, you can think of multiplication & division as a pair and addition & subtraction as a pair. When you see multiplication and division, go left to right, even if division is written first. Same concept with addition and subtraction.

In more mathematical terms, multiplication and division have the same priority. Addition and subtraction have the same priority.

There is a famous PEMDAS problem:

6÷2(1+2)

Most people can get the first step but after that things start to go awry.

6÷2(3)

You must go from left to right and do 6÷2 ~before~ 2*3 because of our left to right priority rule. Then, 3*3 = 9 = the answer.

Answer 3

3. Polynomial Expansions

(a + b)^2 does NOT equal (a^2 + b^2)

it equals (a+b)(a+b) = a^2 + 2ab + b^2

Similar concept with

(a - b)^2

Answer 4

4. Operations using function notation

f(a) - f(b) is generally not equal to f(a-b)

You must calculate f(a) and then f(b) separately, then subtract the values. Similar concept applies to other operations.

Answer 5

5. Operations on multiple functions at once (ex. systems)

Generally, you can multiply both sides of an equation by a constant but you cannot multiply equations in a system together. When you add/subtract them, you must still separate the LHS and RHS of the equations. Furthermore, the rule regarding combining like terms still applies here.

I would lining up the equal signs of the equation and drawing a light, dotted vertical line through the equal sign to keep the sides separate.

Answer 6

-3y + 3y = 0

Answer 7

-4x - 5x = -9x

Answer 8

-11 - 61 = -72

Answer 9

notice how there is still an equal sign separating both sides of the equation

Answer 10

to solve this for x, you would simply divide both sides by -9 and then to solve for y you would re-substitute x back into one of the original equations (either one is fine but in this case I would pick the first one since the arithmetic is cleaner)

Answer 11

Anyway, these are 5 common mistakes I have noticed. I will be glad to answer any questions or provide any additional examples. Thank you for reading and best of luck with your studies.

Answer 12

Fun way to remember PEMDAS:
Pink Elephants March Down A Street c:

Answer 13

Heeeeelpfulll indeeeed.