Adding and Subtracting Polynomials

Question 1

Simplify (p^2 - 9p + 7) + (6p^2 + p - 10).

Accepted Answer

7p^2 - 8p - 3

Answer

7p^4 - 8p^2 - 3

Answer

-5p^2 - 10p + 17

Answer

7p^2 - 8p + 7

Question 2

Simplify (7t^2 + 7t - 3) - (6t^2 - 2t - 9).

Accepted Answer

t^2 + 9t + 6

Answer

t^2 + 5t - 12

Answer

13t^2 + 5t - 12

Answer

-t^2 - 9t - 6

Question 3

Simplify (2u^2 + 4uv - 11v^2) + (4u^2 - 9uv - 4v^2).

Accepted Answer

6u^2 - 5uv - 15v^2

Answer

u^2 - 15v^2

Answer

-2u^2 + 13uv - 7v^2

Answer

-14u^2

Question 4

Simplify (4a^2 - 4a - 9) + (2a^2 - 6a + 9).

Accepted Answer

6a^2 - 10a

Answer

6a^4 - 10a^2

Answer

2a^2 + 2a - 18

Answer

6a^2 - 10a - 9

Question 5

Simplify (5h^2 + 8h + 4) - (7h^2 - 2h - 8).

Accepted Answer

-2h^2 + 10h + 12

Answer

-2h^2 + 6h - 4

Answer

12h^2 + 6h - 4

Answer

2h^2 - 10h - 12

Question 6

Simplify (6t^2 - 6t + 5) + (7t^2 + 8t - 2).

Accepted Answer

13t^2 + 2t + 3

Answer

13t^4 + 2t^2 + 3

Answer

-t^2 - 14t + 7

Answer

13t^2 + 2t + 5

Question 7

Simplify (5t^2 + 5t - 7) - (5t^2 + t - 11).

Accepted Answer

4t + 4

Answer

6t - 18

Answer

10t^2 + 6t - 18

Answer

-4t - 4

Question 8

Simplify (7a^2 - 3a + 7) - (a^2 + 7a + 9).

Accepted Answer

6a^2 - 10a - 2

Answer

6a^2 + 4a + 16

Answer

8a^2 + 4a + 16

Answer

-6a^2 + 10a + 2

Question 9

Simplify (5p^2 + 2pq - 10q^2) + (6p^2 + 6pq - 5q^2).

Accepted Answer

11p^2 + 8pq - 15q^2

Answer

19p^2 - 15q^2

Answer

-p^2 - 4pq - 5q^2

Answer

4p^2

Question 10

Simplify (7h^2 - 3h + 7) - (7h^2 - 6h + 4).

Accepted Answer

3h + 3

Answer

-9h + 11

Answer

14h^2 - 9h + 11

Answer

-3h - 3

Question 11

Simplify (2m^2 - 4mn + 11n^2) + (6m^2 + 6mn - 5n^2).

Accepted Answer

8m^2 + 2mn + 6n^2

Answer

10m^2 + 6n^2

Answer

-4m^2 - 10mn + 16n^2

Answer

16m^2

Question 12

Simplify (4r^2 - 3r - 10) + (2r^2 - 3r + 12).

Accepted Answer

6r^2 - 6r + 2

Answer

6r^4 - 6r^2 + 2

Answer

2r^2 - 22

Answer

6r^2 - 6r - 10

Question 13

A student simplifies (t^2 + 5t + 11) - (6t^2 + 2t + 9) and writes -5t^2 + 7t + 20. What went wrong?

Accepted Answer

only the first term of the second polynomial had its sign changed, and the correct answer is -5t^2 + 3t + 2

Answer

nothing went wrong, and -5t^2 + 7t + 20 is the right answer

Answer

the second polynomial was added instead of subtracted, and the answer is 7t^2 + 7t + 20

Answer

the polynomials were subtracted the wrong way round, and the answer is 5t^2 - 3t - 2

Question 14

Simplify (5n^2 - 7n + 5) + (4n^2 + 5n - 8).

Accepted Answer

9n^2 - 2n - 3

Answer

9n^4 - 2n^2 - 3

Answer

n^2 - 12n + 13

Answer

9n^2 - 2n + 5

Question 15

Simplify (3t^2 + 3t - 11) + (2t^2 + 6t - 9).

Accepted Answer

5t^2 + 9t - 20

Answer

5t^4 + 9t^2 - 20

Answer

t^2 - 3t - 2

Answer

5t^2 + 9t - 11

Question 16

Simplify (3x^2 - 8x - 6) - (4x^2 - 6x + 7).

Accepted Answer

-x^2 - 2x - 13

Answer

-x^2 - 14x + 1

Answer

7x^2 - 14x + 1

Answer

x^2 + 2x + 13

Question 17

Simplify (k^2 - 9k - 7) + (5k^2 + k - 11).

Accepted Answer

6k^2 - 8k - 18

Answer

6k^4 - 8k^2 - 18

Answer

-4k^2 - 10k + 4

Answer

6k^2 - 8k - 7

Question 18

Simplify (4r^2 + 3rs + 10s^2) + (7r^2 + 8rs - 2s^2).

Accepted Answer

11r^2 + 11rs + 8s^2

Answer

22r^2 + 8s^2

Answer

-3r^2 - 5rs + 12s^2

Answer

30r^2

Question 19

Simplify (4p^2 - 8p + 5) - (p^2 - 8p + 8).

Accepted Answer

3p^2 - 3

Answer

3p^2 - 16p + 13

Answer

5p^2 - 16p + 13

Answer

-3p^2 + 3

Question 20

Simplify (7h^2 + 2h - 8) - (4h^2 + 2h - 11).

Accepted Answer

3h^2 + 3

Answer

3h^2 + 4h - 19

Answer

11h^2 + 4h - 19

Answer

-3h^2 - 3

Question 21

Simplify (7b^2 - 8b + 2) + (6b^2 + b - 10).

Accepted Answer

13b^2 - 7b - 8

Answer

13b^4 - 7b^2 - 8

Answer

b^2 - 9b + 12

Answer

13b^2 - 7b + 2

Question 22

Simplify (5h^2 - h + 11) - (3h^2 - 9h - 5).

Accepted Answer

2h^2 + 8h + 16

Answer

2h^2 - 10h + 6

Answer

8h^2 - 10h + 6

Answer

-2h^2 - 8h - 16

Question 23

A student simplifies (a^2 + 8a - 8) - (6a^2 + 4a - 7) and writes -5a^2 + 12a - 15. What went wrong?

Accepted Answer

only the first term of the second polynomial had its sign changed, and the correct answer is -5a^2 + 4a - 1

Answer

nothing went wrong, and -5a^2 + 12a - 15 is the right answer

Answer

the second polynomial was added instead of subtracted, and the answer is 7a^2 + 12a - 15

Answer

the polynomials were subtracted the wrong way round, and the answer is 5a^2 - 4a + 1

Question 24

Simplify (4y^2 + 8y + 5) + (6y^2 - 3y - 8).

Accepted Answer

10y^2 + 5y - 3

Answer

10y^4 + 5y^2 - 3

Answer

-2y^2 + 11y + 13

Answer

10y^2 + 5y + 5

Question 25

Simplify (4n^2 - 5n + 8) - (n^2 + 7n + 9).

Accepted Answer

3n^2 - 12n - 1

Answer

3n^2 + 2n + 17

Answer

5n^2 + 2n + 17

Answer

-3n^2 + 12n + 1

Question 26

Simplify (k^2 + 8k + 8) + (4k^2 - 5k - 8).

Accepted Answer

5k^2 + 3k

Answer

5k^4 + 3k^2

Answer

-3k^2 + 13k + 16

Answer

5k^2 + 3k + 8

Question 27

Simplify (7a^2 + 4ab + 6b^2) - (a^2 - 7ab + 9b^2).

Accepted Answer

6a^2 + 11ab - 3b^2

Answer

6a^2 - 3ab + 15b^2

Answer

8a^2 - 3ab + 15b^2

Answer

17a^2 - 3b^2

Question 28

Simplify (6k^2 - k - 10) - (7k^2 - 2k - 8).

Accepted Answer

-k^2 + k - 2

Answer

-k^2 - 3k - 18

Answer

13k^2 - 3k - 18

Answer

k^2 - k + 2

Question 29

Simplify (5w^2 + 5w + 7) - (7w^2 + 8w + 2).

Accepted Answer

-2w^2 - 3w + 5

Answer

-2w^2 + 13w + 9

Answer

12w^2 + 13w + 9

Answer

2w^2 + 3w - 5

Question 30

Simplify (4m^2 + 6m - 7) + (3m^2 + 2m - 12).

Accepted Answer

7m^2 + 8m - 19

Answer

7m^4 + 8m^2 - 19

Answer

m^2 + 4m + 5

Answer

7m^2 + 8m - 7

Question 31

Simplify (5b^2 + 4b - 8) - (7b^2 - 7b + 3).

Accepted Answer

-2b^2 + 11b - 11

Answer

-2b^2 - 3b - 5

Answer

12b^2 - 3b - 5

Answer

2b^2 - 11b + 11

Question 32

Simplify (4r^2 + 6rs - 7s^2) + (7r^2 - 4rs - 6s^2).

Accepted Answer

11r^2 + 2rs - 13s^2

Answer

13r^2 - 13s^2

Answer

-3r^2 + 10rs - s^2

Answer

0r^2

Question 33

Simplify (4x^2 + 3x + 10) + (6x^2 + 5x - 6).

Accepted Answer

10x^2 + 8x + 4

Answer

10x^4 + 8x^2 + 4

Answer

-2x^2 - 2x + 16

Answer

10x^2 + 8x + 10

Question 34

A student simplifies (2h^2 - 3h + 12) - (7h^2 + 6h - 4) and writes -5h^2 + 3h + 8. What went wrong?

Accepted Answer

only the first term of the second polynomial had its sign changed, and the correct answer is -5h^2 - 9h + 16

Answer

nothing went wrong, and -5h^2 + 3h + 8 is the right answer

Answer

the second polynomial was added instead of subtracted, and the answer is 9h^2 + 3h + 8

Answer

the polynomials were subtracted the wrong way round, and the answer is 5h^2 + 9h - 16

Question 35

Simplify (3n^2 + 8n + 6) + (n^2 - 6n + 10).

Accepted Answer

4n^2 + 2n + 16

Answer

4n^4 + 2n^2 + 16

Answer

2n^2 + 14n - 4

Answer

4n^2 + 2n + 6

Question 36

Simplify (7t^2 - 7t + 3) + (t^2 - 5t + 11).

Accepted Answer

8t^2 - 12t + 14

Answer

8t^4 - 12t^2 + 14

Answer

6t^2 - 2t - 8

Answer

8t^2 - 12t + 3

Question 37

Simplify (7k^2 + k + 9) - (5k^2 - 4k + 8).

Accepted Answer

2k^2 + 5k + 1

Answer

2k^2 - 3k + 17

Answer

12k^2 - 3k + 17

Answer

-2k^2 - 5k - 1

Question 38

Simplify (5m^2 - 3m - 9) + (6m^2 - m + 10).

Accepted Answer

11m^2 - 4m + 1

Answer

11m^4 - 4m^2 + 1

Answer

-m^2 - 2m - 19

Answer

11m^2 - 4m - 9

Question 39

Simplify (4w^2 + 6w + 7) + (2w^2 - 7w - 8).

Accepted Answer

6w^2 - w - 1

Answer

6w^4 - w^2 - 1

Answer

2w^2 + 13w + 15

Answer

6w^2 - w + 7

Question 40

A student simplifies (7w^2 + 4w - 6) - (2w^2 + 4w + 11) and writes 5w^2 + 8w + 5. What went wrong?

Accepted Answer

only the first term of the second polynomial had its sign changed, and the correct answer is 5w^2 - 17

Answer

nothing went wrong, and 5w^2 + 8w + 5 is the right answer

Answer

the second polynomial was added instead of subtracted, and the answer is 9w^2 + 8w + 5

Answer

the polynomials were subtracted the wrong way round, and the answer is -5w^2 + 17

BLASTROOM

BLASTROOM

BLASTROOM

Adding and Subtracting Polynomials

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Adding and Subtracting Polynomials

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner