Exercise 2.3
2. Simplify :
(i)
6a - 3b + 7a + 5b = 6a + 7a - 3b + 5b
= (6 + 7)a + (-3 +
5)b
= 13a + 2b
(ii)
8l – 5l2
– 3l + l2 = (8 – 3)l + (-5 + 1)l2
= 5l - 4l2
(iii)
–z2 +10z2 – 2z +7z2
– 14z = –z2 +10z2 +7z2
– 2z – 14z
= (-1
+ 10 +7)z2 + (-2 - 14)z
= 16 z2 - 16z
(iv)
p – ( p – q ) - q – (q – p) = p – p + q – q - q + p
= p – p + p + q – q – q
= p – q
(v)
3mn
- 3m2 + 4nm - 5n2 - 3m2 + 2n2 = 3mn + 4nm - 3m2 - 3m2 - 5n2 + 2n2
= (3 + 4)mn + (-3 - 3)m2 + (-5 + 2)n2
= 7mn –
6m2 – 3n2
(vi)
(4x2 - 5xy + 3y2) – (3x2 - 2xy
- 4y2) = 4x2 - 5xy + 3y2 - 3x2 + 2xy + 4y2
=
4x2- 3x2 – 5xy + 2xy + 3y2 + 4y2
= (4 – 3)x2
+ (-5 + 2)xy + (3 + 4)y2
=
x2 – 3xy + 7y2
(i)
7ab, 8ab, -
10ab, -
3ab
Solution:
7ab
8ab
- 10ab
- 3ab
-----------2ab
-----------
(ii)
s + t, 2s - t, - s + t
Solution:
s + t
2s – t
- s + t
------------2s + t
------------
(iii)
3a - 2b, 2p + 3q
Solution:
(iv)
2a + 5b + 7,
8a - 3b + 3, - 5a
- 7b – 6
8a - 3b + 3
- 5a - 7b – 6
--------------------5a - 5b + 4
--------------------
(v)
6x + 7y +
3,- 8x - y - 7, 4x - 4y + 2
Solution:
- 8x - y – 7
4x - 4y + 2
-----------------2x + 2y – 2
-----------------
(vi)
6c –
c2 + 3, -3c -
9, c2
+ 4c + 10
Solution:
6c – c2 + 3
-3c +
0 – 9
4c + c2 + 10
--------------------7c + 0 + 4 Ans : 7c + 4
--------------------
– nm2 +
0 + n2 + 3
– 2m2n + mn –
3n2 – 4
--------------------------------3 m2n + 5mn – 4 n2 + 4
--------------------------------
--------------------------------------------------------------------------------------------------------------------------
4. Subtract :
(i)
6a from
14a
Solution:
(ii)
-a2 b from 6a2 b
6a2 b - (-a2 b) = 6a2
b + a2 b
= 7a2b
(iii)
7x2 y2 from -4x2 y2
Solution:
-4x2 y2 - 7x2 y2 = -11x2 y2
(iv)
3xy - 4 from xy + 12
= -2xy + 16
(v)
m(n – 3) from
n(5 – m)
Solution:
n(5 – m)
– [m(n – 3)]
= 5n – mn – mn + 3m
= 5n – 2mn + 3m
(vi)
9p2
- 5p from -10p - 6p2
Solution:
-10p - 6p2 – (9p2 - 5p) = -10p - 6p2 –9p2 + 5p
= -5p – 15p2
(vii)
-3m2 + 6m + 3 from
5m2
- 9
= 8m2 – 6m – 12
(viii)
–s2
+ 12s -
6 from
6s – 10
= s2 - 6s – 4
(ix)
5m2 + 6mn -
3n 2
from 6n2 -
4mn - 4m2
= 9n2 - 10mn – 9m2
5.
(i)
What should be added to 3x2 + xy + 3y2
to
obtain 4x2 + 6xy ?
Solution:
3x2 + xy + 3y2 + Required number = 4x2 + 6xy
Required number = 4x2 + 6xy – (3x2 + xy + 3y2)
= 4x2 + 6xy – 3x2 - xy - 3y2)
= x2 + 5xy – 3y2
(ii)
What should be subtracted from 4p + 6q + 14 to get - 5p + 8q + 20?
Required number = 4p + 6q + 14 – (- 5p
+ 8q + 20)
= 4p + 6q + 14
+ 5p - 8q – 20
= 9p - 2q - 6
(iii)
If
A
= 8x - 3y + 9, B
= - y - 9 and C = 4x - y - 9 find
A
+ B
- C.
A + B – C = (8x - 3y + 9) + (- y - 9) – (4x - y - 9)
= 8x - 3y + 9 - y - 9 – 4x + y
+ 9
= 4x - 3y + 9
6. Three sides of a triangle are 3a + 4b - 2, a - 7 and
2a - 4b + 3. What is its perimeter?
Solution:
Perimeter
of the triangle = (3a + 4b – 2)
+ (a – 7)
+ (2a - 4b + 3)
= 6a – 6 units
7. The sides of a rectangle are 3x + 2 and 5x + 4.
Find its perimeter.
= 2 × (3x + 2 + 5x
+ 4)
= 2 × (8x + 6)
= 16x + 12 units
8. Ram spends Rs. 4a+3 for a shirt and Rs. 8a - 5 for a book. How much does he spend in all?
Solution:
= Rs. 4a + 3 + Rs. 8a – 5
= Rs. 12a – 2
9. A wire is 10x - 3 metres
long. A length of 3x + 5 metres is cut out of it for use. How much
wire is left out?
Solution:
Length
of the wire left out = total length – length cut out
= 10x – 3 – (3x + 5)
= 10x – 3 – 3x – 5
= 7x – 8 metres
10. If A
= p2 + 3p
+ 5 and B
= 2p2 - 5p - 7, then find
(i)
2A
+ 3B = 2 × (p2 + 3p + 5)
+ 3 × (2p2 - 5p - 7)
= 2p2 + 6p + 10 + 6p2
– 15p – 21
= 8p2 – 9p – 11
(ii)
A
- B = p2 + 3p + 5 - (2p2 - 5p - 7)
= p2 + 3p + 5 - 2p2 + 5p + 7
= -p2 + 8p +12
11. Find the value of P - Q + 8 if
P = m2 + 8m and
Q = - m2 + 3m – 2.
Solution:
P - Q + 8 = m2 + 8m - (- m2 + 3m – 2) +
8
= m2 + 8m + m2 - 3m
+ 2
+ 8
= 2m2 + 5m + 10
No comments:
Post a Comment
Leave your valuable comments here....