What should be added to 3x-y+5z^2-4 to get 19y-6-8x ?
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R.D. Sharma Solutions»R.D. Sharma Class 7 Solutions»Chapter 7 Algebraic Expressions»Algebraic Expressions Exercise 7.2
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
Question: 5
Add the following expressions:
(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b
(ii) 5x3 + 7 + 6x - 5x2, 2x2 – 8 - 9x, 4x - 2x2 + 3 x 3, 3 x 3 - 9x - x2 and x - x2 - x3 - 4
Solution:
(i) Required expression = (8a – 6ab + 5b) + (–6a – ab – 8b) + (–4a + 2ab + 3b)
Collecting positive and negative like terms together, we get
8a – 6a – 4a – 6ab – ab + 2ab + 5b – 8b + 3b
= 8a – 10a – 7ab + 2ab + 8b – 8b
= –2a – 5ab
(ii) Required expression = (5 x 3 + 7+ 6x - 5x2) + (2 x 2 – 8 - 9x) + (4x - 2x2 + 3 x 3) + (3 x 3 - 9x-x2) + (x - x2 - x3 - 4)
Collecting positive and negative like terms together, we get
5x3 + 3x3 + 3x3 - x3 - 5x2 + 2x2 - 2x2- x2 - x2 + 6x - 9x + 4x - 9x + x + 7 – 8 - 4
= 10x3 - 7x2 - 7x - 5
Question: 6
Add the following:
(i) x – 3y – 2z
5x + 7y – 8z
3x – 2y + 5z
(ii) 4ab – 5bc + 7ca
–3ab + 2bc – 3ca
5ab – 3bc + 4ca
Solution:
(i) Required expression = (x – 3y – 2z) + (5x + 7y – 8z) + (3x – 2y + 5z)
Collecting positive and negative like terms together, we get
x + 5x + 3x – 3y + 7y – 2y – 2z – 8z + 5z
= 9x – 5y + 7y – 10z + 5z
= 9x + 2y – 5z
(ii) Required expression = (4ab – 5bc + 7ca) + (–3ab + 2bc – 3ca) + (5ab – 3bc + 4ca)
Collecting positive and negative like terms together, we get
4ab – 3ab + 5ab – 5bc + 2bc – 3bc + 7ca – 3ca + 4ca
= 9ab – 3ab – 8bc + 2bc + 11ca – 3ca
= 6ab – 6bc + 8ca
Step-by-step explanation:
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