(a) Add: $p ( p – q), q ( q – r) \text{and} r ( r – p)$

(b) Add: $2x(z-x-y)\text{ and} 2y (z-y-x)$

(c) Subtract: $3l(l-4 m+5 n) \text{from} 4l (10n-3 m+2 l )$

(d) Subtract: $3a(a+b+c )-2b(a-b+c) \text{ from} 4c(-a+b+ c )$

(a) consider the given expressions $p ( p – q), q ( q – r) \text{and} r ( r – p)$.

Add the given expression to get the following,

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

$=p^2+q^2+r^2–pq–qr–pr$

Hence, the simplification of the given expression is $p^2+q^2+r^2–pq–qr–pr$.

(b) consider the given expressions $2x(z-x-y)\text{ and} 2y (z-y-x)$.

Add the given expression to get the following,

$2x (z-x-y) + 2y (z-y-x)= (2xz-2x^2-2xy) + (2yz-2y^2-2xy)$

$= 2xz-4xy+2yz-2x^2-2y^2$

Hence, the simplification of the given expression is $2xz-4xy+2yz-2x^2-2y^2$.

(c) consider the given expressions $3l(l-4 m+5 n) \text{from} 4l (10n-3 m+2 l )$.

Subtract the given expression to get the following,

$4l(10 n-3 m+2l )-3l (l-4 m+5 n)=(40\ln -12lm+8l^2)-(3l^2-12lm+15\ln )$

$=40\ln -12lm+8l^2- 3l^2+12lm -15 \ln$

$=25\ln + 5l^2$

Hence, the simplification of the given expression is $25\ln + 5l^2$.

(d) consider the given expressions $3a(a+b+c )-2b(a-b+c) \text{ from} 4c(-a+b+ c )$.

Subtract the given expression to get the following,

$4c(-a+b+c )-(3a (a+b+c)-2b(a-b+c\left)\right)=(-4ac+4bc+4c^2)- (3a^2+3ab+3ac-( 2ab-2b^2+2bc \left)\right)$

$=-4ac+4bc+4c^2-(3a^2+3ab+3ac-2ab+2b^2- 2bc)$

$=-4ac+4bc+4c^2-3a^2-3ab-3ac+2ab-2b^2+2bc$

$=-7ac+6bc+4c^2-3a^2-ab-2b^2$

Hence, the simplification of the given expression is $-7ac+6bc+4c^2-3a^2-ab-2b^2$.