Add the following
(i) ab - bc, bc - ca, ca - ab
(ii) a - b + ab, b - c + bc , c - a + ac
(iii) 2 p2q2 - 3pq + 4, 5 + 7pq - 3 p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
Solution:
The given algebraic expressions are written by rearranging and combining like terms followed by performing the addition operation as follows:
(i) (ab – bc) + (bc – ca) + (ca - ab)
= ab – bc + bc – ca + ca – ab
= ab – ab – bc + bc – ca + ca
= 0
Thus, the sum of the given expressions is 0.
(ii) (a – b + ab) + (b – c + bc) + (c – a + ac)
= a – b + ab + b – c + bc + c – a + ac
= a – a + b – b + c – c + ab + bc + ca
= 0 + 0 + 0 + ab + bc + ca
= ab + bc + ca
Thus, the sum of the given expressions is ab + bc + ac .
(iii)2p2q2 – 3pq + 4 + 5 + 7pq – 3p2q2
= (2p2q2 – 3pq + 4) + (5 + 7pq – 3p2q2)
= 2p2q2 – 3p2q2 – 3pq + 7pq + 4 + 5
= – p2q2 + 4pq + 9
Thus, the sum of the given expressions is - p2q2 + 4pq + 9.
(iv) (l2 + m2) + (m2 + n2) + (n2 + l2) + (2lm + 2mn + 2nl)
= l2 + l2 + m2 + m2 + n2 + n2 + 2lm + 2mn + 2nl
= 2l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl
= 2(l2 + m2 + n2 + lm + mn + nl )
Thus, the sum of the given expressions is 2(l2 + m2 + n2 + lm + mn + nl ).
☛ Check: NCERT Solutions for Class 8 Maths Chapter 9
Video Solution:
Add the following. (i) ab - bc, bc - ca, ca - ab (ii) a - b + ab, b - c + bc , c - a + ac (iii) 2 p²q² - 3 pq + 4, 5 + 7 pq - 3 p²q² (iv) l² + m², m² + n², n² + l², 2lm + 2mn + 2nl
Maths NCERT Solutions Class 8 Chapter 9 Exercise 9.1 Question 3
Summary:
The sum of the given expressions (i) ab - bc, bc - ca, ca - ab (ii) a - b + ab, b - c + bc , c - a + ac (iii) 2 p2q2 - 3 pq + 4, 5 + 7 pq - 3 p2q2v(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl are (i) 0 (ii) ab + bc + ac (iii) -p2q2 + 4pq + 9 (iv) 2(l2 + m2 + n2 + lm + mn + nl )
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