How do you simplify #3x ( 6x + 2) - 5x ( x - 7y ) - 3( 2x + 5y y )#?

Well, Homework? lol Anyway, this is a long question but it's easily simplified with multiplication, subtraction, addition, and knowing your laws of exponents.

So starting with #3x(6x+2)#. Remember P.E.M.D.A.S. when you are doing any of these expressions!

So we are going to start with distributive property.

#(3x * 6x) + (3x*2)#. So to expand this expression:

#3*x*6*x#, lets just start with #3*6=18#

But what about the #x's?" " 18xxx*x# so simplifying this, it would equal # 18x^2#.

So, overall #3x*6x = 18x^2#.

Now do this with the second part of the bracket.

Below I will do this, if you don't need this explanation again skip this paragraph.

Now, we have to do #3x*2#... again multiply the numbers first,
#3 xx2... =6#.

Since there is only one #x# in this expression it would just be #6x.#
Now we have:
#18x^2+6x # which are unlike terms, so we cannot add them.

Continue doing this through the whole expression:
Then overall you will get:

#color(blue)(3x(6x+2))color(red)(-5x(x-7y)) color(green)(-3(2x+5yy))#
#= color(blue)(18x^2+6x)color(red)(-5x^2+35xy)color(green)(-6x-15y^2)#

Simplify like terms
(to simplify only add/subtract the terms with the same exponents AND letters)

And the answer is the following:
#13x^2+35xy^2-15y^2# (fully simplified)

Hope you understood all of it! Please comment if you have any questions! Also, you can use Mathway.com for answer but, for me, please don't cheat. Use it for your understanding!