"Question 5 (a) Add: p (p − q), q (q − r) and r (r − p) (b) Add: 2x (z − x − y) and 2y (z − y − x) (c) Subtract: 3l (l − 4m + 5n) from 4l (10n − 3m + 2l) (d) Subtract: 3a (a + b + c) − 2b (a − b + c) from 4c (− a + b + c)
Class 8 Algebraic Expressions and Identities Page 146"
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.
Subtraction of algebraic expression:
While Subtracting algebraic expressions we change the sign of the expression which is to be subtracted.
Multiplication of algebraic expression:
The product of two factors with like signs is positive and the product of two factors with unlike signs is negative.
Multiplication of a monomial and the binomial:
If P, q & r are the three monomials we use the distributive law.
p×(q+r)= p×q+ p×r
==========================================================
Solution:
p (p − q), q (q − r) & r (r − p)
(p² - pq) + (q² - qr) + (r²- pr)
= p² + q² + r² - pq - qr – pr
ii) 2x (z − x − y) & 2y (z − y − x)
(2xz - 2x² - 2xy) + (2yz - 2y² - 2xy)
= 2xz - 4xy + 2yz - 2x² - 2y²
iii) 3l (l − 4m + 5n) from 4l (10n − 3m + 2l)
(3l² - 12lm + 15ln) from (40ln - 12lm + 8l²)
= (40ln - 12lm + 8l²) - (3l² - 12lm + 15ln)
While subtracting, we need to remember signs are reversed after –sign once bracket is openedie. + becomes - and - becomes +
= 40ln - 12lm + 8l² - 3l² + 12lm - 15ln
= 40ln - 15ln -12lm + 12lm + 8l² - 3l²
= 25ln + 5l²
iv) 3a (a + b + c) − 2b (a − b + c) from 4c (− a + b + c)
= (3a²+ 3ab + 3ac) -2ab +2b² -2bc from (-4ac + 4bc + 4c²)
= 3a²+ 3ab-2ab+ 3ac+2b² -2bc from (-4ac + 4bc + 4c²)
= 3a²+ab + 3ac+2b² -2bc from (-4ac + 4bc + 4c²)
= (-4ac + 4bc + 4c²) - (3a²+ ab + 3ac +2b² -2bc)
= -4ac + 4bc + 4c² - 3a² -ab - 3ac -2b² +2bc)
= -4ac - 3ac + 4bc +2bc+ 4c² - 3a² -2b²-ab
= -7ac + 6bc + 4c² - 3a² -ab-2b²
= -3a² -2b²+4c²-ab +6bc-7ac
==========================================================
Hope this will help you...