Simplify the following:
(i) 4x - [4y - {x - (2z - 2y) + 3z - (x - 2y - )}]
(ii) 6x – [{2x - 5 (3x - x + 1)) - x - y)
(iii) 10 + 3a - [a + 2b - {3b - a - (a - 2b)}]
(iv) 3a - b + 4c - 2a - 4b + 6c + 2b + 5a - 7c
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Chapter 7: Algebraic Expressions Exercise – 7.2
Question: 1
Add the following:
(i) 3x and 7x
(ii) -5xy and 9xy
Solution:
We have
(i) 3x + 7x = (3 + 7) x = 10x
(ii) -5xy + 9xy = (-5 + 9)xy = 4xy
Question: 2
Simplify each of the following:
(i) 7x3y +9yx3
(ii) 12a2b + 3ba2
Solution:
Simplifying the given expressions, we have
(i) 7x3y + 9yx3 = (7 + 9)x3y = 16x3y
(ii) 12a2b + 3ba2 = (12 + 3)a2b =15a2b
Question: 3
Add the following:
(i) 7abc, -5abc, 9abc, -8abc
(ii) 2x2y, - 4x2y, 6x2y, -5x2y
Solution:
Adding the given terms, we have
(i) 7abc + (-5abc) + (9abc) + (-8abc)
= 7abc – 5abc + 9abc – 8abc
= (7 – 5 + 9 – 8)abc
= (16 – 13)abc
= 3abc
(ii) 2x2y +(-4x2y) + (6x2y) + (-5x2y)
= 2x2y - 4x2y + 6x2y - 5x2y
= (2- 4 + 6 - 5) x 2y
= (8 - 9) x 2y
= -x2y
Question: 4
Add the following expressions:
(i) x3 -2x2y + 3xy2- y3, 2x3- 5xy2 + 3x2y - 4y3
(ii) a4 - 2a3b + 3ab3 + 4a2b2 + 3b4, - 2a4 - 5ab3 + 7a3b - 6a2b2 + b4
Solution:
Adding the given expressions, we have
(i) x3 -2x2y + 3xy2- y3, 2x3- 5xy2 + 3x2y - 4y3
Collecting positive and negative like terms together, we get
x3 +2x3 - 2x2y + 3x2y + 3xy2 - 5xy2 - y3- 4y3
= 3x3 + x2y - 2xy2 - 5y3
(ii) a4 - 2a3b + 3ab3 + 4a2b2 + 3b4, - 2a4 - 5ab3 + 7a3b - 6a2b2 + b4
a4 - 2a3b + 3ab3 + 4a2b2 + 3b4 - 2a4 - 5ab3 + 7a3b - 6a2b2 + b4
Collecting positive and negative like terms together, we get
a4 - 2a4- 2a3b + 7a3b + 3ab3 - 5ab3 + 4a2b2 - 6a2b2 + 3b4 + b4
= - a4 + 5a3b - 2ab3 - 2a2b2 + 4b4