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

1 Answer
Jan 12, 2016

Answer:

#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#