Question

36xy - 39y
------------- < divide line
3y
A. 12x - 13
B. 12x - 13y
C. 32x - 36
D. 36xy2 - 39y2

Answer 1

Similar to teh previuos problem.
Try to factor 3y out of numerator:

\( \dfrac{36xy - 39y}{3y} \)

\( = \dfrac{3y(12x - 13)}{3y} \)

\(= \dfrac{3y}{3y} \times \dfrac{12x - 13}{1} \)

\(= 12x - 13 \)

Answer 2

Okay so you got rid of 36xy-39y or did you divide 36 & 39 by 3 ?

Answer 3

Since the denominator is 3y, I first factored out 3y from the numerator, so that the factored out 3y in the numerator and the 3y in the denmominator can cancel out.

Answer 4

i know that , but i don't see what happened to the 36xy &39y

Answer 5

36xy - 39y = 3y(12x - 13)
^
|------------> 3y factored out

Answer 6

Factoring out is the opposite of multiplying out.

Let me start with a factored out example.

If I ask you to multiply this, what do you get?

2(x + 3) = ?

Answer 7

-6 ? or positive 6 ? lol

Answer 8

I think we need to go one more step back.

What is 2 * 3 = ?

Answer 9

6

Answer 10

Good.
The prodcut of two positive numbers is positive.

What is -2 * 3 = ?

Answer 11

-6

Answer 12

Good.

What is 2 * x?

Answer 13

x would considered 1 ? so it would be 2 right ?

Answer 14

No.
x is not considered 1 or 2.
x stands for an unknown number.

In arithmetic we deal with operations with numbers.
For example: 5 * 2 = 10
-3 + 10 = 7
8/2 = 4
etc.

In algebra, we deal with unknown numbers. Our goal usually is to find out what the unknown number is. In order to solve problems with unknown numbers, we represent the numbers with letters, which we call variables.

x is a letter very often used as a variable.

2 * x means 2 times the number represented by x.
Since we don't know what x stands for, 2 * x is written as 2x.
That is, whatever x is, 2x means t times the number represnted by x.
We can't say that 2x is 2 because we don't know what x is.
If x is 1, then 2x would by 2*1 = 2, but if x is not 1, then 2x is not 2.