Simplify the following.
a) $ (l^{2}-m^{2})(2 l+m)-m^{3} $
b) $ (p+q+r)(p-q+r)+p q-q r $

Given:

a) \( (l^{2}-m^{2})(2 l+m)-m^{3} \)
b) \( (p+q+r)(p-q+r)+p q-q r \)

To do:

We have to simplify the given expressions.

Solutions:

We know that,

$(a+b)(c+d)=a(c+d)+b(c+d)$

Therefore,

a) $(l^{2}-m^{2})(2 l+m)-m^{3}=l^2(2l+m)-m^2(2l+m)-m^3$

$=2l^{2+1}+ml^2-2m^2l-m^{2+1}-m^{3}$

$=2l^.3+ml^2-2m^2l-2m^3$

b) $(p+q+r)(p-q+r)+p q-q r=p(p-q+r)+q(p-q+r)+r(p-q+r)+pq-qr$

$=p^2-pq+pr+pq-q^2+qr+pr-qr+r^2+pq-qr$

$=p^2-q^2+r^2+pq+2pr-qr$