12. If x=1, y=-9, z=6 . Verify
x x [y+ (4)] = [(5) × (-7)] + [5 x z]
Answers
Answer:
Add the following:
(i) 3x and 7x
(ii) −5xy and 9xy
ANSWER:
We have
(i) 3x + 7x = (3 + 7)x = 10x
(ii) -5xy + 9xy = ( -5 + 9)xy = 4xy
Page No 7.13:
Question 2:
Simplify each of the following:
(i) 7x3y + 9yx3
(ii) 12a2b + 3ba2
ANSWER:
Simplifying the given expressions, we have
(i) 7x3y + 9yx3 = (7 + 9)x3y = 16x3y
(ii) 12a2b + 3ba2 = (12 + 3)a2b = 15a2b
Page No 7.13:
Question 3:
Add the following:
(i) 7abc, −5abc, 9abc, −8abc
(ii) 2x2y, − 4x2y, 6x2y, −5x2y
ANSWER:
Adding the given terms, we have
(i) 7abc + (- 5abc) + (9 abc) + (- 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)x2y
= (8 - 9)x2y
= -x2y
Page No 7.14:
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
ANSWER:
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
Page No 7.14:
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+3x3, 3x3−9x−x2 and x−x2−x3−4
ANSWER:
(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 = (5x3 + 7 + 6x - 5x2) + (2x2 - 8 - 9x) + (4x - 2x2 + 3x3) + (3x3- 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
= 11x3 - x3 - 7x2 + 11x - 18x + 7 - 12
= 10x3 - 7x2 - 7x - 5
Page No 7.14:
Question 6:
Add the following:
(i) x−3y−2z5x+7y−8z3x−2y+5z
(ii) 4ab−5bc+7ca−3ab+2bc−3ca5ab−3bc+4ca
ANSWER:
(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 + 11 ca - 3ca
= 6ab - 6bc + 8ca
Page No 7.14:
Question 7:
Add 2x2 − 3x + 1 to the sum of 3x2 − 2x and 3x + 7.
ANSWER:
Sum of 3x2 - 2x and 3x + 7
= (3x2 - 2x) + ( 3x +7)
= 3x2 - 2x + 3x + 7
= (3x2 + x + 7)
Now, required expression = (2x2 - 3x + 1) + (3x2 + x + 7)
= 2x2 + 3x2 - 3x + x + 1 + 7
= 5x2 - 2x + 8
Page No 7.14:
Question 8:
Add x2 + 2xy + y2 to the sum of x2 − 3y2 and 2x2 − y2+ 9.
ANSWER:
Sum of x2 - 3y2 and 2x2 - y2 + 9
= (x2 - 3y2) + (2x2 - y2 + 9)
= x2 + 2x2 - 3y2 - y2+ 9
= 3x2 - 4y2 + 9
Now, required expression = (x2 + 2xy + y2) + (3x2 - 4y2 + 9)
= x2 + 3x2 + 2xy + y2 - 4y2 + 9
= 4x2 + 2xy - 3y2 + 9
Page No 7.14:
Question 9:
Add a3 + b3 − 3 to the sum of 2a3 − 3b3 − 3ab + 7 and −a3 + b3 + 3ab −9.
ANSWER:
First, we need to find the sum of 2a3 - 3b3 - 3ab + 7 and - a3 + b3 + 3ab - 9.
= (2a3 - 3b3 - 3ab + 7) + (- a3 + b3 + 3ab - 9)
Collecting positive and negative like terms together, we get
= 2a3 - a3- 3b3 + b3 - 3ab + 3ab + 7 - 9
= a3 - 2b3 - 2
Now, the required expression = (a3 + b3 - 3) + (a3 - 2b3 - 2).
= a3 + a3 + b3- 2b3 - 3 - 2
= 2a3 - b3 - 5
Page No 7.14:
Question 10:
Subtract:
(i) 7a2b from 3a2b
(ii) 4xy from −3xy
ANSWER:
(i) Required expression = 3a2b - 7a2b
= (3 - 7)a2b
= - 4a2b
(ii) Required expression = - 3 xy - 4xy
= - 7xy
Page No 7.14:
Question 11:
Subtract:
(i) −4x from 3y
(ii) −2x from −5y
ANSWER:
(i) Required expression = (3y) - (-4x)
= 3y + 4x
(ii) Required expression = (-5y) - (-2x)
= -5y + 2x
Step-by-step explanation:
1× [ 9 +4 ] = -35 + 5×6
1×13 = -35 +30
13= -5
-13/5
-2.6