Simplify (p^2+pq-q^2)+(-p^2+3pq+q^2)

$(p^{2} + p q - q^{2}) + (- p^{2} + 3 p q + q^{2})$

Step 1

Remove parentheses.

$p^{2} + p q - q^{2} - p^{2} + 3 p q + q^{2}$

Step 2

Combine the opposite terms in $p^{2} + p q - q^{2} - p^{2} + 3 p q + q^{2}$ .

Subtract $p^{2}$ from $p^{2}$ .

$p q - q^{2} + 0 + 3 p q + q^{2}$

Add $p q - q^{2}$ and $0$ .

$p q - q^{2} + 3 p q + q^{2}$

Add $- q^{2}$ and $q^{2}$ .

$p q + 3 p q + 0$

Add $p q + 3 p q$ and $0$ .

$p q + 3 p q$

Step 3

Add $p q$ and $3 p q$ .

$4 p q$