"Question 3 Add the following.
(i) ab − bc, bc − ca, ca − ab (ii) a − b + ab, b − c + bc, 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
Class 8 Algebraic Expressions and Identities Page 140"
Answers
Algebraic expressions:
A combination of constants and variables connected by any or all of the four fundamental operations +, -,×,÷ is called an algebraic expression..
Terms:
The different parts of the expression separated by the sign+ or – are called the terms of the expression.
Addition of algebraic expressions:
While adding algebraic expressions we collect the like terms and add them.
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Solution:
i) (ab - bc) + (bc - ca) + (ca-ab)
= ab - bc + bc - ca +ca -ab
= ab -ab -bc+bc-ca+ca
= 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+ac
= ab + bc + ca
iii) 2p²q²– 3pq + 4, 5 + 7pq – 3p²q²
= (2p²q²- 3pq + 4) + (5 + 7pq - 3p²q²)
= 2p²q² - 3p²q² - 3pq + 7pq + 4 + 5
= - 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
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Hope this will help you..
Solution:
i) (ab - bc) + (bc - ca) + (ca-ab)
= ab - bc + bc - ca +ca -ab
= ab -ab -bc+bc-ca+ca
= 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+ac
= ab + bc + ca
iii) 2p²q²– 3pq + 4, 5 + 7pq – 3p²q²
= (2p²q²- 3pq + 4) + (5 + 7pq - 3p²q²)
= 2p²q² - 3p²q² - 3pq + 7pq + 4 + 5
= - 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
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