Algebraic Expressions Class 8 Worksheet with Answers
1. Determine which of the following expressions are polynomials:
a. x3 + x7 + x9
b. 2x4 + 1/x2
c.
5x2 +
x
d. 3x2 + x + 7
e. 6x3 + 1/x
2. Write the
degree of each of the following polynomials.
a. –2x3 + 2x2 – 3x + 7
b. 4x4 – 7x + 15
c. 3x5 – 6x3 + 10x – 3
d. 5x3 – 7x
e. 5x3 + 3x2 – 7
f.
7x2 +
7x + 1
g. 2 – 7x – 3x2
h. 4 – 5x –
2x2
+ 3x6
3. Classify
the following algebraic expressions as monomials, binomials or trinomials.
a. 3x5 + 7
b. 7x – 10
c. –2x4 + 4x3
+ 9x
d. –5x2 – 3x + 4
e. 4x2
f. 4x3
g. 3x2 + 4x
h. 2x + 9y
i. x + 2x +
9y
4. Identify the like terms in each of the
following algebraic expressions.
a. 3xy, –4y2,
4c, –7yx, 6y2, 3ab, 2a
b. 9xyz, –3xyz, –4xy,
3xy2, –7y2x, 19yz
c. 6ab, –3bc, 2a,
4bc, –9ba, 2c
d. –2pqr, 7p2r,
–9rp2, 6pqr, 3pr2, 2rp2
5. Add the
following algebraic expressions.
a. 2 – 5abc + 3b2c,
4abc – 7, 2abc – 7b2c + 9
b. 3p2q – 3pq
+ 5, 4pq – 8, 7p + 2p2q + 6
c. 5pqr – 7p2qr
+ 2pq2r, –3p2qr + 9pqr
– 4pr2, 6pr2 – 7pqr
d. 5ab – 6bc + 3ca,
6bc – 4, 4abc – 2ab + 5bc, 2ca – 8
6. Subtract the
following algebraic expressions.
a. 2ab – 3bc from 4ab
– bc
b. 8pqr – 6p2qr
+ 7pq2r – 5pqr2 from 9pqr –
pq2r + 4p2qr – 5pqr2
c. 3x2yz – 7xy2z
+ 9xyz2 – 6 from 5xyz2 + 2xyz – 7x2yz
+ 4xy2z
d. 9abc – 3ab2c
+ 4a2bc – 5abc2 from 5abc2
– 10ab2c + 4a2bc + 2abc
7. Evaluate
the following.
a. –3x3 + 5x2
+10x – 8 for x = –2
b. 2y2 – 3y +
6 for y = –4
c. 12x2y + 4xy2
+ 2xy – 3 for x = 1 and y = 2
8.
Multiply the following:
a. (x + y) by (s + t)
b. (4x +
3y) by (z + 5)
c. (a + b) by (2c – 3d)
d. (5x
– 3y) by (4 – z)
9. Simplify
the following.
a. (p + q + r) (p
– q + r) – p (p + q)
b. (2a – 3b + 7c)
(3a + 6b + c) – a (b + c)
c. x (x + y + z)
– y (y – x + z)
d. (x + y) (x – y + xy) + (x
– y) (x + y – xy)
10.
Divide the following.
a. 6x2 + 12x by 6x
b. 25m7 –
15m3 + 5m2 by 5m2
c. 18x6 – 12x5 + 6x2 by –6x
d. 8a2 + 16a4
– 12a3 by 4a2
11. Using
identities, find the values of the following.
a. (97)2
b. (995)2
c. (75)2
d. (1003)2
12. Find the product using suitable identity.
a. (2x2 + 5) (2x2 – 5)
b.
(4a + 7b) (4a – 7b)
c. (7p – 6q) (7p + 6q)
d. (2xy + 7yz) (2xy +
7yz)
e. (3x + 5z) (3x – 5z)
f. (2m –
7n) (2m – 7n)
13. Find the
value of the following using suitable identity.
a. (53)2
b. 102 × 98
c. 99 × 101
d. (96)2
e. 396 × 404
f. 995
× 1005
14. (4x + 5y)2 – (2x – 3y)2 can be calculated using the identity
a. (a + b)2 = a2 + b2 + 2ab
b. (a – b)2 = a2 + b2 – 2ab
c. a2 – b2 = (a + b) (a – b)
d. None of these
ANSWERS
1. a.
Polynomial
b. Not a polynomial
c. Polynomial
d. Polynomial
e. Not a polynomial
2. a.
3 b. 4
c. 5 d. 3
e. 3 f. 2
g. 2 h. 6
3. a.
Binomial b. Binomial
c. Trinomial d. Trinomial
e. Monomial f. Monomial
g. Binomial h. Binomial
i. Binomial
4. a. Like terms: (3xy, –7yx);
(–4y2, 6y2)
b. Like terms: (9xyz, –3xyz); (3xy2, –7y2x)
c. Like terms: (6ab, –9ba); (–3bc, 4bc)
d. Like terms: (–2pqr, 6pqr); (7p2r,
–9rp2, 2rp2)
5. a. abc – 4b2c
+ 4
b. 3p2q – 3pq + 5, 4pq – 8, 7p
+ 2p2q + 6
c. 7pqr – 10p2qr + 2pq2r
+ 2pr2
d. 3ab + 5bc + 5ca + 4abc – 12
6. a. 2ab + 2bc
b. pqr – 8pq2r + 10p2qr
c. 2xyz – 4xyz2 – 10x2yz +
11xy2z + 6
d. 10abc2 – 7ab2c – 7abc
7. a.
16 b. 50
c. 41
8. a. xs
+ xt + ys + yt
b. 4xz + 20x + 3yz +
15y
c. 2ac – 3ad + 2bc – 3bd
d. 20x – 5xz – 12y + 3yz
9. a. 2pr
– q2 + r2 – pq
b. 6a2 – 18b2
+ 7c2 + 2ab + 22ac + 39bc
c. x2 – y2
+ 2xy + xz – yz
d. 2x2
– 2y2 + 2xy2
10. a. x +
2
b. 5m5 – 3m + 1
c. -3x5 + 2x4
– x
d. 2 + 4a2 – 3a
11. a.
9409 b. 9,90,025
c. 5625 d. 10,06,009
12. a. 4x4
– 25
b. 16a2 – 49b2
c. 49p2 – 36q2
d. 4x2y2
+ 49y2z2 + 28xy2z
e. 9x2 – 25z2
f. 4m2 + 49n2
– 28mn
13. a.
2809 b. 9996
c. 9999 d. 9216
e. 1,59,984
f. 9,99,975
14. c
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