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3.Add the following :
(i) \(ab – be, be – ca, ea – ab\)

(ii)\( a – b + ab, b-c + be, c – a + ac\)

(iii) \(2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2\)

(iv)\( l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl\)


Answer :

(i) We have the expressions as:\( ab – bc, bc – ca, ca – ab\)
Adding them :

\((ab – bc) + (bc – ca) + (ca – ab) \)

\(\Rightarrow ab – bc + bc – ca + ca – ab \)

\(\Rightarrow (ab – ab) + (bc – bc) + (ca – ca)\quad\) [Placing the like terms together]

\(\Rightarrow 0 + 0 + 0\)

\(\Rightarrow 0\)

(ii) We have the expressions as:\(a – b + ab, b – c + bc, c – a + ac\)

Adding these we have:

\((a – b + ab) + (b – c + bc) + (c – a + ac) \)

\(\Rightarrow a – b + ab + b – c + bc + c – a + ac\)

\(\Rightarrow (a – a) + (b – b) + (c – c) + ab + bc + ac\quad \)[Placing all the like terms together]

\(\Rightarrow 0 + 0 + 0 + ab + bc + ac\)

\(\Rightarrow ab + bc + ac\)

(iii)We have the expressions as:\(2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2\)

Adding these we get: \(2p^2q^2 – 3pq + 4 + 5 + 7pq – 3p^2q^2\)

\(\Rightarrow (2p^2q^2– 3p^2q^2)+(– 3pq+ 7pq)+ (4 + 5)\quad\)[Placing like terms together]

\(\Rightarrow -p^2q^2 + 4pq+ 9\)

(iv)We have the expressions as:\( l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl\)
Adding these we get: \((l^2 + m^2)+( m^2 + n^2)+( n^2 + l^2)+ (2lm + 2mn + 2nl)\)

\(\Rightarrow (l^2+l^2)+ (m^2+m^2)+ (n^2+n^2)+(2lm + 2mn + 2nl)\quad\)[Placing like terms together]

\(\Rightarrow (2l^2)+ (2m^2)+ (2n^2)+(2lm + 2mn + 2nl\)

\(\Rightarrow 2(l^2+ m^2+n^2+lm + mn + nl)\)

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