Question

Factor the entire expression completely: 10n^3 − 15n^2 + 20xn^2 − 30xn

Answer 1

@AZ can u help?

Answer 2

We have to factor by grouping



can you factor out the GCF from \( 10n^2 - 15n^2\)

Answer 3

\( 10n^3 - 15n^2\) **

Answer 4

\[5n^2\]

Answer 5

Good and what do you get when you factor it out?

Answer 6

umm 2n - 3

Answer 7

Good!! Now similarly, can you factor \( 20xn^2 -30xn\)

Answer 8

This is what we currently have

Answer 9

ok, I got 2n - 3

Answer 10

what did you factor out?

Answer 11

uh I did 10xn??

Answer 12

Good!! That's correct

Answer 13

So now you got it
5x^2(2x-3) + 10xn(2n-3)
Can you un-distribute it

Answer 14

*n, not x._.

Answer 15

so, I think the answer would be (2n-3)(5n^2 + 10xn)

Answer 16

So do you see how you have 2n - 3 in the parenthesis?

Think of the 2n-3 as like an apple or 'a'

so

\( 5n^2 \color{red}{(2n-3)} + 10xn\color{red}{(2n-3)}\)

Answer 17

\(\color{#0cbb34}{\text{Originally Posted by}}\) @carmelle
so, I think the answer would be (2n-3)(5n^2 + 10xn)
\(\color{#0cbb34}{\text{End of Quote}}\)

Yup that's correct!

Answer 18

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
\(\color{#0cbb34}{\text{Originally Posted by}}\) @carmelle
so, I think the answer would be (2n-3)(5n^2 + 10xn)
\(\color{#0cbb34}{\text{End of Quote}}\)

Yup that's correct!
\(\color{#0cbb34}{\text{End of Quote}}\)
Thank you!!

Answer 19

Just for completion sake, what I was trying to say

you can think of it as it's own term so

\( 5n^2 \color{red}{(2n-3)} + 10xn\color{red}{(2n-3)}\)


\( 5n^2 \color{red}{(a)} + 10xn\color{red}{(a)}\)

And then you factor it out

\( \color{red}{a}( 5n^2 + 10xn)\)

And you replace it back with the original (2n-3) that we had switched out with 'a' just to make it easier to see

\( \color{red}{(2n-3)}( 5n^2 + 10xn)\)

Answer 20

so good job!! :)

Answer 21

ok, got it~