Question

How do you simplify `(3x-y)(5x+y)`?

Answer 1

`15x^2-2xy-y^2`

Explanation:

Given: `color(brown)((3x-y)color(blue)((5x+y))`

The trick is to realize that everything inside one bracket is multiplied by everything inside the other. DO NOT FORGET ABOUT THE SIGNS.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Rewrite as: `color(brown)(3xcolor(blue)((5x+y)) -y color(blue)((5x+y))`

Giving: `color(brown)( (3x xxcolor(blue)(5x))+(3x xxcolor(blue)(y))-(y xx color(blue)(5x))-(y xxcolor(blue)(y))`

Notice that multiplying by `color(brown)(-y)` changes the sign of everything inside `color(blue)((5x+y))`

`15x^2+3xy-5xy-y^2`

`15x^2-2xy-y^2`