Worksheet on Addition and Subtraction of Polynomials will assist students to learn the concept of addition, subtraction of polynomials. Polynomials play a key role in laying the foundation for several topics related to algebra and students need to know about how to perform arithmetic operations on them.

Access the numeric questions available in the Adding and Subtracting Polynomials Worksheet that are well structured and practice using them on a regular basis. The Math Printable Worksheet for Adding and Subtracting Polynomials will develop logical and reasoning skills among you.

I. Simplify the following polynomial expressions:

(i) (10x2-5x+5)+(8x+10)
(ii) Take 3a + 9b – c from 7a + 12b – 4c

Solution:

(i) Given (10x2-5x+5)+(8x+10)
Arrange the like terms together and then add,
=10x2-5x+8x+5+10
=10x2+3x+15
Hence, By simplifying (10x2-5x+5)+(8x+10) we get 10x2+3x+15.
(ii) Take 3a + 9b – c from 7a + 12b – 4c
i.e. we have to Subtract 3a + 9b – c from 7a + 12b – 4c.
=7a+12b-4c-(3a+9b-c)
=7a+12b-4c-3a-9b+c
=7a-3a+12b-9b-4c+c
=4a+3b-3c
Hence, By simplifying 3a + 9b – c from 7a + 12b – 4c we get 4a+3b-3c.

II. The sum of two expressions is 5x2 – 4xy + 2y2. If one of them is 3x2 + y2, find the other?

Solution:

Given,
The sum of the two expressions is= 5x2 – 4xy + 2y2
one of the expression is=3x2 +y2Let the other expression be p(x).
3x2 + y2+P(x)=5x2 – 4xy + 2y2
p(x)=5x2 – 4xy + 2y2-(3x2 + y2)
p(x)=5x2 – 4xy + 2y2-3x2 – y2
=2x2 -4xy+y2
Therefore, the other expression is 2x2 -4xy+y2.

III. Evaluate the following expressions
i) ( 15a2 + 10a − 6a ) + (25a + 10)
ii) On adding 14a2 +8𝑎4 with 3a2+ 2a4+4

Solution:

i) Given ( 15a2 + 10a − 6a ) + (25a + 10)
=15a2 + 10a − 6a+25a+10
=15a2+29a+10
Hence, By adding ( 15a2 + 10a − 6a ) + (25a + 10) we get 15a2+29a+10.
ii) add 14a2 +8𝑎4 ,3a2+ 2a4+4
=14a2 +8𝑎4+3a2+ 2a4+4
=17a2+10𝑎4+4
Hence, By adding 14a2 +8𝑎4 ,3a2+ 2a4+4 we get 17a2+10𝑎4+4.

IV. Subtract the following polynomial expression
(-150a2-54a+5)-(34a2+66a)

Solution:

Given, (-150a2-54a+5)-(34a2+66a)
=-150a2-54a+5-34a2-66a
=-184a2-120a+5
Hence, By subtracting 34a2+66a from -150a2-54a+5 we get -184a2-120a+5.

V. Solve the following

i) How much is 4x + 2y greater than x – 2y?
ii) How much should p + 2q – r be increased to get 5p+q?

Solution:

i) Subtract x-2y from 4x+2y.
=4x+2y-(x-2y)
=4x+2y-x+2y
=4x-x+4y
=3x+4y
Hence, 4x + 2y greater than x – 2y by 3x+4y.
ii) Let p + 2q – r be increased by x.
p+2q-r+x=5p+q
x=5p+q-(p+2q-r)
=5p+q-p-2q+r
=4p-q+r
Hence, p + 2q – r be increased to 4p-q+r to get 5p+q.

VI. From the sum of 5x + y – 8z and 2y – 4z, subtract 2x – y – 3z.

Solution:

Sum of 5x + y – 8z and 2y – 4z is
=5x + y – 8z+2y-4z
=5x+3y-12z
Subtract 2x – y – 3z from 5x+3y-12z
=5x+3y-12z-(2x – y – 3z)
=5x+3y-12z-2x+y+3z
=3x+4y-9z
Hence, By subtracting 2x – y – 3z from the sum of 5x + y – 8z and 2y – 4z we get 3x+4y-9z.

VII. Subtract 2x – 3y – z from the sum of 6x – 7y + 2z and 2x + y – 4z.

Solution:

Sum of 6x – 7y + 2z and 2x + y – 4z is=6x-7y+2z+2x+y-4z
=6x+2x-7y+y+2z-4z
=8x-6y-2z
Now, Subtract 2x – 3y – z from 8x-6y-2z.
=8x-6y-2z-(2x-3y-z)
=8x-2x-6y+3y-2z+z
=6x-3y-z
Hence, By subtracting 2x – 3y – z from the sum of 6x – 7y + 2z and 2x + y – 4z is 6x-3y-z.

VIII. By how much 8a2 – 2b2 be diminished to give 3a2 + b2?

Solution:

Let the value be x.
x-(8a2 – 2b2)=3a2 + b2
x=3a2 + b2 +(8a2 – 2b2)
x=11a2-b2
Therefore, 11a2-b2 be diminished to give 3a2 + b2.

IX. Subtract m2 – 5n + 7 from 4m2 + 2n and add your result to m2+ n – 1.

Solution:

Subtract m2 – 5n + 7 from 4m2 + 2n
=4m2 + 2n-(m2 – 5n + 7)
=4m2 + 2n-m2 + 5n -7
=4m2-m2+2n+5n-7
=3m2+7n-7
Add 3m2+7n-7 to m2+ n – 1.
=3m2+7n-7+m2+ n – 1
=4m2+8n-8
Therefore, the sum of 3m2+7n-7 and m2+ n – 1 is 4m2+8n-8.

x. Subtract 2m2n – 3n2 from 6m2n– 2mn2+ 8n2 and subtract your result from the sum of the two expressions 3mn2 + 5n2 – 2m2n and m2n + 5m2 – 2mn2.

Solution:

Subtract 2m2n – 3n2 from 6m2n– 2mn2+ 8n2
=6m2n– 2mn2+ 8n2-(2m2n-3n2)
=6m2n-2m2n-2mn2+8n2+3n2
=4m2n-2mn2+11n2
The sum of the two expressions 3mn2 + 5n2 – 2m2n and m2n + 5m2 – 2mn2 is
= 3mn2 + 5n2 – 2m2n + m2n + 5m2 – 2mn2
=3mn2-2mn2+5n2-2m2n + m2n + 5m2
=mn2– m2n +5m2 + 5n2
Subtract 4m2n-2mn2+11n from mn2– m2n +5m2 + 5n2
=mn2– m2n +5m2 + 5n2– (4m2n-2mn2+11n2)
=mn2+2mn2-m2n-4m2n+5m2+5n2-11n2
=3mn2-5m2n+5m2-6n2
Therefore, the result is 3mn2-5m2n+5m2-6n2.