Question

Choose the correct simplification of the expression (3x − 6)(2x^2 − 4x − 5).

6x^3 − 24x^2 + 9x − 30
6x^3 + 9x + 30
6x^3 − 24x^2 + 9x + 30
6x^3 − 24x^2 + 39x + 30

Answer 1

Completely confused

Answer 2

\((3x − 6)(2x^2 − 4x − 5)\)
So here you want to distribute

Answer 3

Okay okay hold on imma write it down

Answer 4

Okay

Answer 5

Okay done

Answer 6

\[(\color{red}{3x}\color{blue}{-6})(2x^2-4x-5)=\]
\[(\color{red}{3x}\times 2x^2)+(\color{red}{3x}\times-4x)+(\color{red}{3x}\times-5)+(\color{blue}{-6}\times2x^2)+(\color{blue}{-6}\times-4x)+(\color{blue}{-6}\times-5) \]

Answer 7

Latex cut off RIP

Answer 8

\[(\color{red}{3x}\color{blue}{-6})(2x^2-4x-5)=\]
\[(\color{red}{3x}\times 2x^2)+(\color{red}{3x}\times-4x)+(\color{red}{3x}\times-5)+\\(\color{blue}{-6}\times2x^2)+(\color{blue}{-6}\times-4x)+(\color{blue}{-6}\times-5) \]

Answer 9

Got it just writing it down :)

Answer 10

Okie done

Answer 11

Well just simplify those

Answer 12

Do you know how to do that?

Answer 13

Multiply the ones in () and then add?

Answer 14

Oh wait idk shoot o.o

Answer 15

Yes multiply the ones in parenthesis

Answer 16

What about the ones that are like 3x * -5

Answer 17

Multiply the number only, so it would be -15x

Answer 18

So is this right?

\[6x^{2} + 12x + 15 - 12x ^{2} + 24x + 30\]

Answer 19

When multiplying exponents you add the exponent
ex. \(x\times x^2=x^3\)

Answer 20

so 6x^2 would become 6x^3?

Answer 21

Right

Answer 22

Alright lemme fix

Answer 23

Okay done

Answer 24

Okay, what do you have?

Answer 25

\[6x^3 - 12x + 15x - 12x^3 + 24x + 30\]

Answer 26

Almost
\((\color{red}{3x}\times 2x^2)=6x^3 ~~\\
+(\color{red}{3x}\times-4x)=-12x^2\\
+(\color{red}{3x}\times-5)=-15x\\
+(\color{blue}{-6}\times2x^2)=-12x^3\\+
(\color{blue}{-6}\times-4x)=24x\\
+(\color{blue}{-6}\times-5)=30\)

Answer 27

ohh

Answer 28

The power adding applies to all exponents
\(x\times x=x^2\)
\(x\times x^3=x^4\)
\(number~\times x=numberx\)

Answer 29

time to rewrite

Answer 30

Alright i think i got it now

Answer 31

Okay

Answer 32

Idk what to do now ;-;

Answer 33

Add the numbers that have the same power of x
ex. \(2x+5+3x+9\) = \(5x+14\)
This applies to app powers!

Answer 34

So like 6x³ - 12x^3 ?

Answer 35

would the exponets add?

Answer 36

Yes, add the co-efficients

Answer 37

No exponents stay the same

Answer 38

So like this?
6x^3 + 12x^3 = 18x^3

Answer 39

Right

Answer 40

Okay so this is what i got.

\[18x^3 - 12x^2 - 39x + 30\]

Answer 41

Ah! i goofed previously!

\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
Almost
\((\color{red}{3x}\times 2x^2)=6x^3 ~~\\
+(\color{red}{3x}\times-4x)=-12x^2\\
+(\color{red}{3x}\times-5)=-15x\\
+(\color{blue}{-6}\times2x^2)=-12x^3\\+
(\color{blue}{-6}\times-4x)=24x\\
+(\color{blue}{-6}\times-5)=30\)
\(\color{#0cbb34}{\text{End of Quote}}\)


\(+(\color{blue}{-6}\times2x^2)=-12x^3\)

Correction:
\(+(\color{blue}{-6}\times2x^2)=-12x^2\)

Answer 42

Now i am confused...............

Answer 43

I made a mistake, in
\(+(\color{blue}{-6}\times2x^2)=-12x^3\)

I told you about the exponents rule right?
I accidentally added an exponent here

-6 doesn't have an x, so the \(x^2\) stays the same

Answer 44

This was just a mistake from my end

Answer 45

so it would be 18x^2?

Answer 46

\(6x^3\color{red}{-12x^2}-15x-12x^3+24x+30\) is your equation


only the red segment is the change

Answer 47

Alright i fixed it

Answer 48

So now i do the same that i just did with adding them?

Answer 49

Yes

Answer 50

so 6x^3 + -12x^3?

Answer 51

\(-12x^3\) is \(-12x^2\) when I corrected myself
So \(6x^3\) stays like that


\(6x^3-12x^2-15x-12x^2+24x+30\)

Answer 52

Oh yeah dang it my bad

Answer 53

\[6x^3 - 12x^2 - 12x^2 - 15x + 24x + 30\]

so like this^^^^

Answer 54

Right

Answer 55

both of the 12x^2 would cancel out?

Answer 56

They are both negative, they would add up

Answer 57

so it would end up being 24x^2?

Answer 58

-24x^2, yes, keep the sign

Answer 59

Okay

Answer 60

\[6x^3 - 24x^2 - 9x +30\]
Like this?

Answer 61

Close, when adding −15x+24x

You want to keep the sign of the greater number

Answer 62

so positive

Answer 63

Right

Answer 64

I got it now

Answer 65

So the answer would be C?

Answer 66

Yep

Answer 67

THANK YOUUUUUUUU

Answer 68

Iḿma end up writing it all back out and neater so i can get it again :D. Thanks again!

Answer 69

Okay, sure!