Adding, Subtracting, Multiplying and Dividing Polynomials Worksheet 1
1.
Write an algebraic expression for the
following:
a.
Four times a number, increased by seventeen.
b.
Product of 6 and a number, decreased by 4.
2.
Add:
a.
5x, 7x and 11x
b.
7pq, 4pq and 3pq
c.
–7abc, 4abc, –12abc and 15abc
d.
–3a, –5a and –10a
e.
15xy, –5xy and –7xy
3.
Multiply the following:
a.
4ab by 3a
b.
–15x by –4x
c.
–5x3yz by –3xy2z
d.
16a2b3c2 by –4a2b2c2
4. Subtract: 3x + y – 2z from
5x + 3y
5.
Substitute x = 3 and y = 1 and
find the value of x2 – 10x + 25 + 5y – 3.
6.
Choose the correct answer for each of the following.
a.
Two terms may be added only if the terms are
i. unlike
ii. like
iii. same degree
iv. same numerals
b.
The product of a constant and a variable is
i. constant
ii. variable
iii. coefficient
iv. monomial
c.
The sum of 3x2y and 4y2x is
i. 7x2y
ii. 7y2x
iii. 3x2y + 4y2x
iv. 12x3y3
d.
Simplify: 5x + 3y + 4 + 3x + 2y – 2
i. 8x + 5y + 2
ii. 15x2 + 6y2 – 8
iii. 8x + 5y + 6
iv. 15xy + 6xy – 8
e.
– 10abc × –5ab2c is equal to
i. 50abc
ii. –50a2b2c2
iii. 50a2b3c2
iv. –50a2b2c
7.
Add: 5ab – 2bc + 6bc, 2ab + 4bc –
3bc, – ab + 2bc – 3bc
8.
What must be added with 2x – 3y +
4z to get x + y + z?
9.
Multiply: x2 + 5x – 4
by – 2x
Adding, Subtracting, Multiplying and Dividing Polynomials Worksheet 2
1.
Write the algebraic expression for:
a.
seven increased by a number x
b.
thirty-nine decreased by a number y
2.
Match each of the following to the correct
options:
a.
a + b/2 is a i.
3xy
b.
Subtracting 2x + 3y – 4z from 4x + 5y + 6z,
the result is ii.
binomial
c.
21x2y2z2 ÷ 7xyz2
is equal to
iii. 9a2 – 4b2
d.
Simplifying x2 + 2 – 3x2 – 6 + 2x2, the result
is iv. 2x + 2y + 10z
e.
(3a + 2b) × (3a – 2b) is v. –4
3.
Multiply the following:
a.
5x + 4y by 2xy
b.
3x2 – 5y2 by 4x2y2
c.
4a + 3b by a + b
4.
Evaluate the following when x = 2, y
= 3, z = 1:
a.
x + y + z
b.
2x – 3y + 2z
c.
5xy + yz – zx
5.
Subtract the following:
a.
xy – yz + zx from 4xy + 5yz + 6zx
b.
4a + 5b + c from 5a + 6b + 3c
6.
Multiply 5ab – 2bc by ac –
4bc.
7.
Fill in the blanks of each of the following:
a.
2x + 3y – z – 2x – 2y + z is equal to
___________.
b.
x2 × x3 is equal to ___________.
c.
3a – 5a is equal to ___________.
d.
2x × –2y is equal to ___________.
e.
–3x – 4x is equal to ___________.
8.
Add using vertical method:
a.
2x – 5y + 4z, 5x + 9y – 6z, 4x +
4y – 5z
b.
6x + 5y + 7z, 5x – 2y + z
c.
5xy – 3yz + 2zx, 2xy – 3yz + 5zx and
–3xy + 2yz – 4zx
d.
4a + 5b +6c, a – b + c, a – b
+ c, – a + b – c
e.
ab + bc + ac, –2ac + bc + 5ab
9.
Find the value of xyz/100 if x =
1500, y = 6 and z = 3.
10. From the sum of 3a + 4b – 5c and 4a +
7b + 6c, subtract 6a – 3b + 5c.
Adding, Subtracting, Multiplying and Dividing Polynomials Worksheet 3
1.
Divide the following:
a. 81a3b2c
– 72ab2c3 + 9a2b2c2
by 9a2b2c2
b. –x4y5
+ 5x2y3 + 10x3y2
by 5xyz
2.
Fill in the blanks:
a.
2x + 8x – 5x = ___________
b.
3x2y × 5xy3 = ___________
c.
If x = 1, then 6x2 – x – 5 = ___________
d.
2a + 3b – 4b + 6a = ___________
e.
The degree of the term 3x2y3 is
___________.
3.
Find the degree of the following polynomials:
a.
9x2y2 + 7xy3 + 5x3y
– 3x4y2
b.
2ab3 – 3a2b2 + 5a2b
– 6a4b
4.
Subtract:
a.
3a + 5b – c from 7a + 4b + 2c
b.
a – b + 4c from 5a – 4b + 8c
c.
x2 + 2ax + a2 from x2
+ a2
5.
Evaluate the following when x = –2, y
= –1, z = 1.
a.
x2 + 2y2 – 3z2
b.
3xyz + 5x + 3y – 4z
6.
Multiply the following:
a.
3x – 2y by 2x + y
b.
4xy – 5x2y2 by x – y
c.
–3ab + 7bc by –2a + 3b
7.
What must be added to 3x – 2y +
5z to get x + y – z?
8.
Multiply: – 6x2y3
by –2x3y2
9.
State true or false:
a.
7x2y2, 18x2y2
and –5x2y2 cannot be added as their
numerical coefficients are unlike.
b.
Two algebraic terms can be multiplied only if they are like terms.
c.
8x + 15 is greater than 8x + 2.
d.
If there is no sign between two algebraic terms, it means multiply as xy.
e.
If p = 1, q = 3, then p + q – pq is equal to
1.
10.
Add the following using horizontal method:
a.
4a + 2b, 3a – 5b
b.
5x + 3y + 2z, 7x + 4y + 5z
c.
2x – 3y + z, 5x + 4y – 2z
d.
x + 4y + 3z, 2x + 7y + z and x +
y + 6z
e.
ab + 3bc – 4ac, 2ab + 5bc + 2ac and 7ab
– 2bc + 3ac
ANSWERS
Worksheet 1
1. a. 4x + 17 b. 6x – 4
2. a. 23x b.
14pq
c. 0 d.
-18 e. 3xy
3. a. 12a2b b.
60x2
c. 15x4y3z2
d. -64a4b5c4
4. 2x + 2y +
2z
5. 6
6. a. ii b. ii
c. iii
d. i
e. iii
7. 6ab + 4bc
8. –x + 4y – 3z
9. –2x3 – 10x2 + 8x
Worksheet 2
1. a. 7 + x b. 39 – y
2. a. ii b. iv c.
i
d. v e. iii
3. a. 10x2y + 8xy2
b. 12x4y2
– 20x2y4
c. 4a2 + 7ab
+ 3b2
4. a. 6 b. -4 c. 31
5. a. 3xy + 6yz + 5zx
b. a + b + 2c
6. 5a2bc – 2abc2 – 20ab2c + 8b2c2
7. a. y b. x5
c. -2a d. -4xy
e. -7x
8. a. 11x + 8y – 7z
b. 11x + 3y + 8z
c. 4xy – 4yz + 3zx
d. 6a + 4b + 7c
e. 6ab + 2bc – ac
9. 270
10. a + 14b – 4c
Worksheet 3
1. a. 9a/c – 8c/a + 1
b. -x3y4/5z
+ xy2/z + 2x2y/z
2. a. 5x b. 15x3y4
c. 0 d.
8a – b
e. 5
3. a. 6 b. 5
4. a. 4a – b + 3c
b. 4a – 3b + 4c
c. -2ax
5. a. 3 b. -11
6. a. 6x2 – xy – 2y2
b. 4x2y – 5x3y2
– 4xy2 + 5x2y3
c. 6a2b – 14abc
– 9ab2 + 21b2c
7. -2x + 3y – 6z
8. 12x5y5
9. a. False b. False
c. True d. True
e. True
10. a. 7a – 3b
b. 12x + 7y + 7z
c. 7x + y – z
d. 4x + 12y 10z
e. 10ab + 6bc + ac
MCQs Questions for Class 6 Maths
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| Maths Worksheets for Other Chapters of Class 6 |
1. Knowing our numbers class 6 worksheets
2. Integers questions for class 6
3. HCF and LCM questions for class 6
4. Fraction questions for class 6
6. Exponents and powers extra questions
7. Algebraic expressions for class 6 worksheets
8. Linear equations in one variable questions for class 6
9. Ratio and proportion class 6 worksheet
10. Percentage questions for class 6
12. Simple interest questions for class 6
13. Basic geometrical ideas class 6 worksheet
14. Worksheet on angles for class 6
15. Parallel lines and transversal worksheet
17. Triangles worksheet for class 6
18. Construction questions for class 6
19. Symmetry class 6 worksheet
20. Perimeter and area class 6 worksheets
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1. Sets maths class 6 worksheets
2. Adding, subtracting, multiplying and dividing polynomials worksheets
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