Adding, Subtracting, Multiplying and Dividing Polynomials Worksheets

Adding, Subtracting, Multiplying and Dividing Polynomials Worksheets

Let us solve Adding, Subtracting, Multiplying and Dividing Worksheets.

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.

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 ___________.

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 6x2x – 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

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

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