Question

I WILL GIVE A MEDAL AND FAN YOU!
Factor Completely: 12a3d2 − 6ad3.

Prime

6a3d3(2a − d)

6ad2(2ad − d)

6ad2(2a2 − d)

Answer 1

Is this your question?
\(12a^3d^2 - 6ad^3\)

Answer 2

Yes Ma'am

Answer 3

So, look for common terms. Start with the coefficients.

Answer 4

I meant common factors, sorry.

Answer 5

So like the 6a and the 12a?

Answer 6

Yes, but you will be dividing so only use the terms that will divide evenly.

Answer 7

First look at 6.

Answer 8

Can you divide both terms by 6?

Answer 9

Yes

Answer 10

Its the last one:

Answer 11

Thank you

Answer 12

I know that i can divide it by 12 by 6

Answer 13

yw!

Answer 14

So divide both terms by 6. Look at what you have left and see what else you can divide both terms by.

Answer 15

which ones are the terms :(

Answer 16

One term is \(12a^3d^2\) and the other is \(6ad^3\)

Answer 17

Ohh So dividing 12/6 and divide 6/6

Answer 18

Yes. Then look at the variables and see what else you can factor out.

Answer 19

well there are two of these ^3

Answer 20

\(6(2a^3d^2 - ad^3)\)

Answer 21

It is the variables you are looking at, not their exponents. You cannot factor out an exponent separate from its variable.

Answer 22

ohh so there are two a's and two d's

Answer 23

sorry i thought i been entered that

Answer 24

Each term can be divided by a and by d, the question is how many of each can be factored out.

Answer 25

Sorry, you did mention the a earlier. I must have missed it.

Answer 26

lol

Answer 27

when they say factor , what does that stand for?

Answer 28

2 and 3 are factors of 6.
\(2 \times 3 = 6\)
Factors are the numbers (or variables) that multiply together to make a product(the answer of multiplication).

Answer 29

Ohhh

Answer 30

So, You've factored out a 6 and now you want to factor out an a. What does that leave you with inside the parenthesis?

Answer 31

2a^2-d?

Answer 32

\(6(2a^3d^2 - ad^3)\) Only 1 a can be factored out so divide each term by a. Remember when you are dividing the same base with different exponents, you will subtract the exponents.

Answer 33

Ohh well that makes more sense

Answer 34

So, \(\Large{\frac{2a^3d^2}{a}} = \)what?

Answer 35

Then do the same with the other term.

Answer 36

how could they be divided by a variable?

Answer 37

All the numbers and variables in the term are being multiplied so when you divide them, it is just like canceling numbers. Let me try to demonstrate:
\[\frac{4\times2 \times 3}{3 \times 6 \times 2}\]
You can divide the 2 by 2 and the 3 by 3 and end up with \(\frac{4}{6}\).

Answer 38

Ohh and just be left with 4/6

Answer 39

but what about the bottom?

Answer 40

its only a variable

Answer 41

Do you see what is left?

Answer 42

yes 2a^2d^2

Answer 43

like that?

Answer 44

Ok, now do the same to the other term.