what is the answer of question 3

3.) The product of 3 less than twice x and 2 more than the quantity 3 times x...we can think of this as:

Product of (2x - 3) and (3x + 2)...3 less than twice x is the same as twice x - 3 or 2x - 3 & 2 more than the quantity 3 times x is the same as 3 times x plus 2 = 3x + 2 -->

(2x - 3)*(3x + 2)

Now, FOIL: first, outside, inside, & last -->

first: 6x^2

outside: 4x

inside: -9x

last: -6

Add all the terms: 6x^2 + 4x - 9x - 6...lastly, simplify by collecting "like" terms -->

D, 6x^2 - 5x - 6.

4.) [(5x(x+1)^2) / (x^3(x^3 + 9x))] * [(x^2 + 9) / (x + 1)]

Notice, we can get rid of the (x+1)'s leaving us with:

5x(x+1) / x^3(x^3 + 9x) * [(x^2 + 9)]

5x(x+1) / x^3*x(x^2 + 9) * [(x^2 + 9)]

5x(x+1) / x^4(x^2 + 9) * [(x^2 + 9)]

5x(x+1) / x^4

Get rid of the x in 5x by taking away 1 x from x^4:

C, 5(x+1) / x^3.

I can't understand why you put it 

 (2x - 3) and (3x + 2)

My answer is the same as Ninja's and Ninja is very good at explaining things but maybe a different presentation will help.  

3 less than twice x is (2x-3)  I just put it in brackets to make it clear

and

2 more than the quatity 3 times x is (3x+2)

and product means multiply

so the product of these is 

(2x-3)*(3x+2) = (2x-3)(3x+2)

and when you expand that out you get

$$(2x-3)(3x+2)\\
=2x(3x+2)-3(3x+2)\\
=6x^2+4x-9x-6\\
=6x^2-5x-6$$

Is that any clearer??  If not let us know and we will explain some more. 

Now my problem is to understand the expressions 3 less than twice x  You know that English is not my mother language =D  .. What is less than mean ! 

Look at it this way.....if I gave you "2 less than 5"...isn't that just 5 - 2??

Then, "twice x "  is just 2x

And three less than "twice x" is just....... 2x - 3

Does that make sense??

Now its clear ... thanx for all 

Thanks Chris   ,  sorry 15x3 there has been a lot of questions and I only just got back to yours. 

In question 3 we multiply the two brackets  because the word " and " in the question ؟ 

I'm waiting !!! 

We multiply them because it says represents the product of.

Thanx