Page No 84:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
________
â
Page No 84:
Question 2:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
________
â
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
_____
Page No 84:
Question 3:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
_____
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
___________
Page No 84:
Question 4:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
___________
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
Page No 84:
Question 5:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
Page No 84:
Question 6:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
Answer:
On arranging the terms of the given expressions in the descending powers of and adding column-wise:
Page No 84:
Question 7:
On arranging the terms of the given expressions in the descending powers of and adding column-wise:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise:
Page No 84:
Question 8:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise:
Answer:
On arranging the terms of the given expressions in the descending powers of and adding column-wise:
Page No 84:
Question 9:
On arranging the terms of the given expressions in the descending powers of and adding column-wise:
Answer:
On arranging the terms of the given expressions in the descending powers of and subtracting:
Page No 84:
Question 10:
On arranging the terms of the given expressions in the descending powers of and subtracting:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 11:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 12:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 13:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 14:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 15:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Answer:
On arranging the terms of the given expressions in the descending powers of and subtracting column-wise:
Page No 84:
Question 16:
On arranging the terms of the given expressions in the descending powers of and subtracting column-wise:
Answer:
Arranging the terms of the given expressions in the descending powers of and subtracting column-wise:
Page No 84:
Question 17:
Arranging the terms of the given expressions in the descending powers of and subtracting column-wise:
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 18:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Answer:
Let the required number be .
∴ Required number =
Page No 84:
Question 19:
Let the required number be .
∴ Required number =
Answer:
Sides of the rectangle are and .
Perimeter of the rectangle is .
Page No 84:
Question 20:
Sides of the rectangle are and .
Perimeter of the rectangle is .
Answer:
Let be the three sides of the triangle.
∴ Perimeter of the triangle =
Given perimeter of the triangle =
One side () =
Other side () =
Perimeter =
Thus, the third side is .
Page No 87:
Question 1:
Let be the three sides of the triangle.
∴ Perimeter of the triangle =
Given perimeter of the triangle =
One side () =
Other side () =
Perimeter =
Thus, the third side is .
Answer:
By horizontal method:
Page No 87:
Question 2:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 3:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 4:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 5:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 6:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 7:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 8:
By horizontal method:
Answer:
By horizontal method:
i.e
Page No 87:
Question 9:
By horizontal method:
i.e
Answer:
By horizontal method:
Page No 87:
Question 10:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 11:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 12:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 13:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 14:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 15:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 16:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 17:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 18:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 19:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 20:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 21:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 22:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 23:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 24:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 25:
By horizontal method:
Answer:
By horizontal method:
Page No 87:
Question 26:
By horizontal method:
Answer:
By horizontal method:
Page No 90:
Question 1:
By horizontal method:
Answer:
(i) 24x2y3 by 3xy
Therefore, the quotient is
8xy2.(ii) 36xyz2 by −9xz
Therefore, the quotient is
−
4yz.
(iii)
Therefore, the quotient is 6
xy.
(iv) −56
mnp2 by 7
mnp
Therefore, the quotient is −8
p.
Page No 90:
Question 2:
(i) 24x2y3 by 3xy
Therefore, the quotient is
8xy2.(ii) 36xyz2 by −9xz
Therefore, the quotient is
−
4yz.
(iii)
Therefore, the quotient is 6
xy.
(iv) −56
mnp2 by 7
mnp
Therefore, the quotient is −8
p.
Answer:
(i) 5m3− 30m2 + 45m by 5m
Therefore, the quotient is m2− 6m + 9.
(ii) 8x2y2 − 6xy2 + 10x2y3 by 2xy
Therefore, the quotient is 4xy − 3y + 5xy2.
(iii) 9x2y − 6xy + 12xy2 by − 3xy
Therefore, the quotient is −3x + 2 − 4y.
(iv) 12x4 + 8x3 − 6x2 by − 2x2
2-4x+32
Therefore the quotient is −6x2 − 4x + 3.
Page No 90:
Question 3:
(i) 5m3− 30m2 + 45m by 5m
Therefore, the quotient is m2− 6m + 9.
(ii) 8x2y2 − 6xy2 + 10x2y3 by 2xy
Therefore, the quotient is 4xy − 3y + 5xy2.
(iii) 9x2y − 6xy + 12xy2 by − 3xy
Therefore, the quotient is −3x + 2 − 4y.
(iv) 12x4 + 8x3 − 6x2 by − 2x2
2-4x+32
Therefore the quotient is −6x2 − 4x + 3.
Answer:
Therefore, the quotient is
and the remainder is 0.
Page No 90:
Question 4:
Therefore, the quotient is
and the remainder is 0.
Answer:
Therefore, the quotient is
−2 and the remainder is 0.
Page No 90:
Question 5:
Therefore, the quotient is
−2 and the remainder is 0.
Answer:
(x2 + 12x + 35) by (x + 7)
Therefore, the quotient is and the remainder is 0.
Page No 90:
Question 6:
(x2 + 12x + 35) by (x + 7)
Therefore, the quotient is and the remainder is 0.
Answer:
Therefore, the quotient is
and the remainder is 0.
Page No 90:
Question 7:
Therefore, the quotient is
and the remainder is 0.
Answer:
Therefore, the quotient is
and the remainder is 0.
Page No 90:
Question 8:
Therefore, the quotient is
and the remainder is 0.
Answer:
Therefore, the quotient is
and the remainder is 7.
Page No 90:
Question 9:
Therefore, the quotient is
and the remainder is 7.
Answer:
Therefore, the quotient is
and the remainder is 1.
Page No 90:
Question 10:
Therefore, the quotient is
and the remainder is 1.
Answer:
Therefore, the quotient is
-x+1 and the remainder is 0.
Page No 90:
Question 11:
Therefore, the quotient is
-x+1 and the remainder is 0.
Answer:
Therefore, the quotient is (
x2 - 3
x + 4) and remainder is 0.
Page No 90:
Question 12:
Therefore, the quotient is (
x2 - 3
x + 4) and remainder is 0.
Answer:
Therefore, the quotient is (
x-1) and the remainder is 0.
Page No 90:
Question 13:
Therefore, the quotient is (
x-1) and the remainder is 0.
Answer:
Therefore, the quotient is ( 5
x+ 3) and the remainder is (
x + 1).
Page No 90:
Question 14:
Therefore, the quotient is ( 5
x+ 3) and the remainder is (
x + 1).
Answer:
Therefore, the quotient is (
x-1) and the remainder is 0.
Page No 90:
Question 15:
Therefore, the quotient is (
x-1) and the remainder is 0.
Answer:
Therefore, the quotient is ( 4
x2+ 3
x -2) and the remainder is (
x-1).
Page No 93:
Question 1:
Therefore, the quotient is ( 4
x2+ 3
x -2) and the remainder is (
x-1).
Answer:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Page No 93:
Question 2:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Answer:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Page No 93:
Question 3:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Answer:
We shall use the identities (a+b)2 =a2 +b2 +2ab and (a-b)2 =a2 +b2 -2ab.
(i) We have:
(ii)We have:
(iii) We have :
(iv) We have:
(v) We have:
(vi) We have:
(vii) We have:
(viii) We have:
(ix) We have:
Page No 94:
Question 4:
We shall use the identities (a+b)2 =a2 +b2 +2ab and (a-b)2 =a2 +b2 -2ab.
(i) We have:
(ii)We have:
(iii) We have :
(iv) We have:
(v) We have:
(vi) We have:
(vii) We have:
(viii) We have:
(ix) We have:
Answer:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
(vii) We have:
(viii) We have:
(ix) We have:
Page No 94:
Question 5:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
(vii) We have:
(viii) We have:
(ix) We have:
Answer:
We shall use the identity (a+b)2 =a2 +b2 +2ab.
(i)
(ii)
(iii)
(iv)
Page No 94:
Question 6:
We shall use the identity (a+b)2 =a2 +b2 +2ab.
(i)
(ii)
(iii)
(iv)
Answer:
We shall use the identity (a-b)2 = a2 +b2 -2ab.
(i)
(ii)
(iii)
(iv)
Page No 94:
Question 7:
We shall use the identity (a-b)2 = a2 +b2 -2ab.
(i)
(ii)
(iii)
(iv)
Answer:
We shall use the identity (a-b) (a+b)=a2 - b2.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Page No 94:
Question 8:
We shall use the identity (a-b) (a+b)=a2 - b2.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Therefore, the value of the expression (9
x2 + 24
x + 16), when
x = 12, is 1600.
Page No 94:
Question 9:
Therefore, the value of the expression (9
x2 + 24
x + 16), when
x = 12, is 1600.
Answer:
Therefore, the value of the expression (64
x2 + 81
y2 + 144
xy), when
x = 11 and
y = , is 10000.y=43
Page No 94:
Question 10:
Therefore, the value of the expression (64
x2 + 81
y2 + 144
xy), when
x = 11 and
y = , is 10000.y=43
Answer:
Page No 94:
Question 11:
Answer:
Therefore, the value of
x2+
is 14.
Therefore, the value of
x4+
is 194.
Page No 94:
Question 12:
Therefore, the value of
x2+
is 14.
Therefore, the value of
x4+
is 194.
Answer:
Page No 94:
Question 13:
Answer:
Page No 94:
Question 14:
Answer:
Page No 94:
Question 15:
Answer:
Page No 94:
Question 1:
Answer:
(c) (−6a + 17b)
Page No 95:
Question 2:
(c) (−6a + 17b)
Answer:
(d) (3p2 + 5q − 9r3 +7)
Page No 95:
Question 3:
(d) (3p2 + 5q − 9r3 +7)
Answer:
(d) x2 + 2x − 15
Page No 95:
Question 4:
(d) x2 + 2x − 15
Answer:
(b) (6x2 + 7x − 3)
Page No 95:
Question 5:
(b) (6x2 + 7x − 3)
Answer:
(c) (x2 + 8x + 16)
Page No 95:
Question 6:
(c) (x2 + 8x + 16)
Answer:
(d) (x2 − 12x + 36)
Page No 95:
Question 7:
(d) (x2 − 12x + 36)
Answer:
(b) (4x2 − 25)
Page No 95:
Question 8:
(b) (4x2 − 25)
Answer:
(c) −4ab2
Page No 95:
Question 9:
(c) −4ab2
Answer:
(b) (2x + 1)
Page No 95:
Question 10:
(b) (2x + 1)
Answer:
(a) (x − 2)
Page No 95:
Question 11:
(a) (x − 2)
Answer:
(c) (a4 − 1)
Page No 95:
Question 12:
(c) (a4 − 1)
Answer:
a)
(1x2−1y2)
Page No 95:
Question 13:
a)
(1x2−1y2)
Answer:
(c) 23
Page No 95:
Question 14:
(c) 23
Answer:
(b) 38
Page No 95:
Question 15:
(b) 38
Answer:
(c) 6400
[using the identity (a-b)(a+b)=a2 -b2]
Page No 95:
Question 16:
(c) 6400
[using the identity (a-b)(a+b)=a2 -b2]
Answer:
(a) 39991
[using the identity (a+b) (a-b) = a2 -b2]
Page No 95:
Question 17:
(a) 39991
[using the identity (a+b) (a-b) = a2 -b2]
Answer:
(b) 116
Page No 95:
Question 18:
(b) 116
Answer:
(a) 67
Page No 95:
Question 19:
(a) 67
Answer:
(c) 625
View NCERT Solutions for all chapters of Class 8