Question

Part A

Directions: Add the following polynomials by combining like terms. Do not worry about putting them into simplest form just yet.

1. (10b8 + 3ab7 + c + 9abc + 4b2) + (1 + c + 4ab7 + 9b2)

2. (13xy7 + 11yz9 + x + 9 + 8xy2) + (yz9 + 13xy7 + x + 10 + xy2)

3. (5 + n + 4mo2 + 8n8) + (19 + 16mo2 + 4n10 + 9mno2) + (45 + n)

4. (15yz3 + 13xy7 + x + 9 + 4x2) + (1 + x + 4xy7 + 8yz3)

5. (9ab7 + bc + 14ab3 + 9a + 4ab2) + (1 + a + 16ab3+ 4ab7 +bc + 9ab2)

6. (12 + r + 6s4t2 + 8st2) + (19 + 16s2 + 4st7 + 6s4t2 + st2) + (8s4t2 + 15 + r)

7. (3xy2+ 6yx5 + 11yz9 + y + 87) + (13yx5 + 13xy2 + y + 10 + yx5)

8. (n2 + 4 + 403 + n) + (4 + n + 4m2n2 + 8n2) + (18 + 9m2n2 + 403 + 9n2)

9. (12 +6s4t2 +s) + (10 + s + 6s4t2 + 8s2) + (21+ 6s4t2 + 7s4t2)

10.(13yx5) + (13xy2 + 19y + 3z9) + (x + yz9+ 8yx5) + (yz9 + 43xy2 + 11y + 6z9+ xy2)

Part B

Directions: Next, put each of the following polynomials, which you’ve already added together, into simplest form by ordering the degrees of each term correctly. Hint: you should use your answers from the above problems.

11. (10b8 + 3ab7 + c + 9abc + 4b2) + (1 + c + 4ab7 + 9b2)

12. (13xy7 + 11yz9 + x + 9 + 8xy2) + (yz9 + 13xy7 + x + 10 + xy2)

13. (5 + n + 4mo2 + 8n8) + (19 + 16mo2 + 4n10 + 9mno2) + (45 + n)

14. (15yz3 + 13xy7 + x + 9 + 4x2) + (1 + x + 4xy7 + 8yz3)

15. (9ab7 + bc + 14ab3 + 9a+ 4ab2) + (1 + a + 16ab3+ 4ab7 +bc + 9ab2)

16. (12 + r + 6s4t2 + 8st2) + (19 + 16s2 + 4st7 + 6s4t2 + st2) + (8s4t2 + 15 + r)

17. (3xy2+ 6yx5 + 11yz9 + y + 87) + (13yx5 + 13xy2 + y + 10 + yx5)

18. (n2 + 4 + 403 + n) + (4 + n + 4m2n2 + 8n2) + (18 + 9m2n2 + 403 + 9n2)

19. (12 +6s4t2 +s) + (10 + s + 6s4t2 + 8s2) + (21+ 6s4t2 + 7s4t2)

20. (13yx5) + (13xy2 + 19y + 3z9) + (x + yz9+ 8yx5) + (yz9 + 43xy2 + 11y + 6z9+ xy2)

Answer 1

(10b^8 + 3ab^7 + c + 9abc + 4b^2) + (1 + c + 4ab^7 + 9b^2)

Result: 10b^8 + 7ab^7 + 2c + 9abc + 13b^2 + 1

(13xy^7 + 11yz^9 + x + 9 + 8xy^2) + (yz^9 + 13xy^7 + x + 10 + xy^2)

Result: 26xy^7 + 11yz^9 + 2x + 19 + 9xy^2 + yz^9

(5 + n + 4mo^2 + 8n^8) + (19 + 16mo^2 + 4n^10 + 9mno^2) + (45 + n)

Result: 16mo^2 + 4n^10 + 9mno^2 + 53 + 2n + 8n^8

(15yz^3 + 13xy^7 + x + 9 + 4x^2) + (1 + x + 4xy^7 + 8yz^3)

Result: 13xy^7 + 8yz^3 + 5x^2 + 2x + 10

(9ab^7 + bc + 14ab^3 + 9a + 4ab^2) + (1 + a + 16ab^3 + 4ab^7 + bc + 9ab^2)

Result: 5ab^7 + 30ab^3 + 10ab^2 + 10a + 2bc + 1

(12 + r + 6s^4t^2 + 8st^2) + (19 + 16s^2 + 4st^7 + 6s^4t^2 + st^2) + (8s^4t^2 + 15 + r)

Result: 8s^4t^2 + 6st^7 + 16s^2 + 4st^2 + 47 + 2r

(3xy^2 + 6yx^5 + 11yz^9 + y + 87) + (13yx^5 + 13xy^2 + y + 10 + yx^5)

Result: 6yx^5 + 13xy^2 + 13yx^5 + 11yz^9 + 2y + 97

(n^2 + 4 + 403 + n) + (4 + n + 4m^2n^2 + 8n^2) + (18 + 9m^2n^2 + 403 + 9n^2)

Result: 13n^2 + 8m^2n^2 + 415 + 18

(12 + 6s^4t^2 + s) + (10 + s + 6s^4t^2 + 8s^2) + (21 + 6s^4t^2 + 7s^4t^2)

Result: 18s^4t^2 + 7s^4t^2 + 15s^2 + 9s + 43

(13yx^5) + (13xy^2 + 19y + 3z^9) + (x + yz^9 + 8yx^5) + (yz^9 + 43xy^2 + 11y + 6z^9 + xy^2)

Result: 21yx^5 + 14xy^2 + y + 3z^9 + yz^9 + 6z^9 + x

Part B: Simplifying the Polynomials

10b^8 + 7ab^7 + 2c + 9abc + 13b^2 + 1

26xy^7 + 11yz^9 + 2x + 19 + 9xy^2 + yz^9

16mo^2 + 4n^10 + 9mno^2 + 53 + 2n + 8n^8

13xy^7 + 8yz^3 + 5x^2 + 2x + 10

5ab^7 + 30ab^3 + 10ab^2 + 10a + 2bc + 1

8s^4t^2 + 6st^7 + 16s^2 + 4st^2 + 47 + 2r

6yx^5 + 13xy^2 + 13yx^5 + 11yz^9 + 2y + 97

13n^2 + 8m^2n^2 + 415 + 18

18s^4t^2 + 7s^4t^2 + 15s^2 + 9s + 43

21yx^5 + 14xy^2 + y + 3z^9 + yz^9 + 6z^9 + x

Answer 2

Please mark as brilliant if I am right.. :)

Explanation:

Part A: Adding the Polynomials (combining like terms)

(10b^8 + 3ab^7 + c + 9abc + 4b^2) + (1 + c + 4ab^7 + 9b^2)

Result: 10b^8 + 7ab^7 + 2c + 9abc + 13b^2 + 1

(13xy^7 + 11yz^9 + x + 9 + 8xy^2) + (yz^9 + 13xy^7 + x + 10 + xy^2)

Result: 26xy^7 + 11yz^9 + 2x + 19 + 9xy^2 + yz^9

(5 + n + 4mo^2 + 8n^8) + (19 + 16mo^2 + 4n^10 + 9mno^2) + (45 + n)

Result: 16mo^2 + 4n^10 + 9mno^2 + 53 + 2n + 8n^8

(15yz^3 + 13xy^7 + x + 9 + 4x^2) + (1 + x + 4xy^7 + 8yz^3)

Result: 13xy^7 + 8yz^3 + 5x^2 + 2x + 10

(9ab^7 + bc + 14ab^3 + 9a + 4ab^2) + (1 + a + 16ab^3 + 4ab^7 + bc + 9ab^2)

Result: 5ab^7 + 30ab^3 + 10ab^2 + 10a + 2bc + 1

(12 + r + 6s^4t^2 + 8st^2) + (19 + 16s^2 + 4st^7 + 6s^4t^2 + st^2) + (8s^4t^2 + 15 + r)

Result: 8s^4t^2 + 6st^7 + 16s^2 + 4st^2 + 47 + 2r

(3xy^2 + 6yx^5 + 11yz^9 + y + 87) + (13yx^5 + 13xy^2 + y + 10 + yx^5)

Result: 6yx^5 + 13xy^2 + 13yx^5 + 11yz^9 + 2y + 97

(n^2 + 4 + 403 + n) + (4 + n + 4m^2n^2 + 8n^2) + (18 + 9m^2n^2 + 403 + 9n^2)

Result: 13n^2 + 8m^2n^2 + 415 + 18

(12 + 6s^4t^2 + s) + (10 + s + 6s^4t^2 + 8s^2) + (21 + 6s^4t^2 + 7s^4t^2)

Result: 18s^4t^2 + 7s^4t^2 + 15s^2 + 9s + 43

(13yx^5) + (13xy^2 + 19y + 3z^9) + (x + yz^9 + 8yx^5) + (yz^9 + 43xy^2 + 11y + 6z^9 + xy^2)

Result: 21yx^5 + 14xy^2 + y + 3z^9 + yz^9 + 6z^9 + x

Part B: Simplifying the Polynomials

10b^8 + 7ab^7 + 2c + 9abc + 13b^2 + 1

26xy^7 + 11yz^9 + 2x + 19 + 9xy^2 + yz^9

16mo^2 + 4n^10 + 9mno^2 + 53 + 2n + 8n^8

13xy^7 + 8yz^3 + 5x^2 + 2x + 10

5ab^7 + 30ab^3 + 10ab^2 + 10a + 2bc + 1

8s^4t^2 + 6st^7 + 16s^2 + 4st^2 + 47 + 2r

6yx^5 + 13xy^2 + 13yx^5 + 11yz^9 + 2y + 97

13n^2 + 8m^2n^2 + 415 + 18

18s^4t^2 + 7s^4t^2 + 15s^2 + 9s + 43

21yx^5 + 14xy^2 + y + 3z^9 + yz^9 + 6z^9 + x