Question

Add following.
(i) $ab-bc,bc-ca,ca-ab$
(ii) $a-b+ab,b-c+bc,c-a+ac$
(iii) $2p^2{q}^2-3pq+4,5+7pq-3p^2{q}^2$
(iv) $l^2+m^2,m^2+n^2,n^2+l^2,2lm+2mn+2nl$

Answer 1

(i) Given $(ab-bc)+(bc-ca)+(ca-ab)$
$=ab-bc+bc-ca+ca-ab$
Grouping the like terms as
$=ab-ba+bc-bc+ca-ca$
All terms gets cancelled, So
$=0$
Hence, the addition of given expression is $0$

(ii) Given $(a-b+ab)+(b-c+bc)+(c-a+ac)$

$=a-b+ab+b-c+bc+c-a+ac$
Grouping the like terms as

$=a-a+b-b+c-c+ab+bc+ca$
By simplifying, we get

$=ab+bc+ac$

(iii) Given $(2p^2{q}^2-3pq+4)+(5+7pq-3p^2{q}^2)$

$=2p^2{q}^2-3pq+4+5+7pq-3p^2{q}^2$
Grouping the like terms, we get

$=2p^2{q}^2-3p^2{q}^2+7pq-3pq+5+4$
By simplifying, we get

$=-p^2{q}^2+4pq+9$

(iv) Given $(l^2+m^2)+(m^2+n^2)+(n^2+l^2)+(2lm+2mn+2nl)$
Grouping the like terms, we get

$=l^2+l^2+m^2+m^2+n^2+n^2+2lm+2mn+2nl$

$=2l^2+2m^2+2n^2+2(lm+mn+nl)$
By simplifying, we get

$=2(l^2+m^2+n^2+lm+mn+nl)$