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Algebraic Expressions
Use the given algebraic expression to complete the table of number patterns.
S. No |
Expression |
Terms |
|||||||||
1st |
2nd |
3rd |
4th |
5th |
… |
10th |
… |
100th |
… |
||
(i) |
2n − 1 |
1 |
3 |
5 |
7 |
9 |
– |
19 |
– |
– |
– |
(ii) |
3n + 2 |
2 |
5 |
8 |
11 |
– |
– |
– |
– |
– |
– |
(iii) |
4n + 1 |
5 |
9 |
13 |
17 |
– |
– |
– |
– |
– |
– |
(iv) |
7n + 20 |
27 |
34 |
41 |
48 |
– |
– |
– |
– |
– |
– |
(v) |
n2 + 1 |
2 |
5 |
10 |
17 |
– |
– |
– |
– |
10, 001 |
– |
The given table can be completed as follows.
S.No. |
Expression |
Terms |
|||||||||
1st |
2nd |
3rd |
4th |
5th |
… |
10th |
… |
100th |
… |
||
(i) |
2n − 1 |
1 |
3 |
5 |
7 |
9 |
– |
19 |
– |
199 |
– |
(ii) |
3n + 2 |
2 |
5 |
8 |
11 |
17 |
– |
32 |
– |
302 |
– |
(iii) |
4n + 1 |
5 |
9 |
13 |
17 |
21 |
– |
41 |
– |
401 |
– |
(iv) |
7n + 20 |
27 |
34 |
41 |
48 |
55 |
– |
90 |
– |
720 |
– |
(v) |
n2 + 1 |
2 |
5 |
10 |
17 |
26 |
– |
101 |
– |
10,001- |
– |
Sponsor Area
Identify like terms in the following:
(a) −xy2, − 4yx2, 8x2, 2xy2, 7y, − 11x2, − 100x, −11yx, 20x2y, −6x2, y, 2xy,3x
(b) 10pq, 7p, 8q, − p2q2, − 7qp, − 100q, − 23, 12q2p2, − 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2
Simplify combining like terms:
(i) 21b − 32 + 7b − 20b
(ii) − z2 + 13z2 − 5z + 7z3 − 15z
(iii) p − (p − q) − q − (q − p)
(iv) 3a − 2b − ab − (a − b + ab) + 3ab + b − a
(v) 5x2y − 5x2 + 3y x2 − 3y2 + x2 − y2 + 8xy2 −3y2
(vi) (3 y2 + 5y − 4) − (8y − y2 − 4)
Add:
(i) 3mn, − 5mn, 8mn, −4mn
(ii) t − 8tz, 3tz − z, z − t
(iii) − 7mn + 5, 12mn + 2, 9mn − 8, − 2mn − 3
(iv) a + b − 3, b − a + 3, a − b + 3
(v) 14x + 10y − 12xy − 13, 18 − 7x − 10y + 8xy, 4xy
(vi) 5m − 7n, 3n − 4m + 2, 2m − 3mn − 5
(vii) 4x2y, − 3xy2, − 5xy2, 5x2y
(viii) 3p2q2 − 4pq + 5, − 10p2q2, 15 + 9pq + 7p2q2
(ix) ab − 4a, 4b − ab, 4a − 4b
(x) x2 − y2 − 1 , y2 − 1 − x2, 1− x2 − y2
Subtract:
(i) − 5y2 from y2
(ii) 6xy from − 12xy
(iii) (a − b) from (a + b)
(iv) a (b − 5) from b (5 − a)
(v) − m2 + 5mn from 4m2 − 3mn + 8
(vi) − x2 + 10x − 5 from 5x − 10
(vii) 5a2 − 7ab + 5b2 from 3ab − 2a2 −2b2
(viii) 4pq − 5q2 − 3p2 from 5p2 + 3q2 − pq
(a) What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?
(b) What should be subtracted from 2a + 8b + 10 to get − 3a + 7b + 16?
What should be taken away from 3x2 − 4y2 + 5xy + 20 to obtain
− x2 − y2 + 6xy + 20?
(a) From the sum of 3x − y + 11 and − y − 11, subtract 3x − y − 11.
(b) From the sum of 4 + 3x and 5 − 4x + 2x2, subtract the sum of 3x2 − 5x and − x2 + 2x + 5.
If p = −2, find the value of:
(i) 4p + 7
(ii) −3p2 + 4p + 7
(iii) −2p3 − 3p2 + 4p + 7
Sponsor Area