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

Jan 12, 2016

$15 {x}^{2} - 2 x y - {y}^{2}$

#### 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.
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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 $\textcolor{b r o w n}{- y}$ changes the sign of everything inside $\textcolor{b l u e}{\left(5 x + y\right)}$

$15 {x}^{2} + 3 x y - 5 x y - {y}^{2}$

$15 {x}^{2} - 2 x y - {y}^{2}$