Question

Help me understand this simplification please.

Answer 1

\[\large\rm 2x(2x+3)(24+32x)\quad=\quad 2x(2x+3)\color{orangered}{(32x+24)}\]So pay attention to this orange portion :)

Answer 2

Hmm what can we factor out of it?
What do those two terms share?

Answer 3

2 or 2x's?

Answer 4

32 and 24?
Hmm I think we can take an 8 from each, ya?

Answer 5

Oh oh oh, the part you underlined isn't the whole change that was made,
lemme add some more of that top line.

Answer 6

\[\large\rm 2(3+4x)^2(4x+3)-2x(2x+3)\color{orangered}{(32x+24)}\]So does this step make sense to you?
\[\large\rm 2(3+4x)^2(4x+3)-2x(2x+3)\color{orangered}{\cdot8(4x+3)}\]

Answer 7

yes

Answer 8

Now what we'll do is,
we'll place some square brackets around the whoooole thing,\[\large\rm \left[\color{royalblue}{2}(3+4x)^2\color{royalblue}{(4x+3)}-\color{royalblue}{2}x(2x+3)\cdot8\color{royalblue}{(4x+3)}\right]\]And our next step is to factor out the common stuff these two huge terms have in common.
I've highlighted it in blue so it's clearer.

Answer 9

Do you see how they each have a 2?
and they each have a (4x+3)?

Answer 10

Yes

Answer 11

So when we pull that stuff out, we get,\[\large\rm \color{royalblue}{2(4x+3)}\left[(3+4x)^2-x(2x+3)\cdot8\right]\]

Answer 12

and we just "put" the 8 at the x to be 8x?

Answer 13

Multiplication is commutative (we can multiply in any order, rearrange)
so yes,\[\large\rm ab\cdot c=acb=cba\]Any order, bring the 8 to the front with the x :)

Answer 14

It's all just multiplication within that big clump

Answer 15

ok, I got it. Thank you for typing it all out. :)

Answer 16

cool! ୧ʕ•̀ᴥ•́ʔ୨