Algebraic expressions · Ages 13–14

Adding and subtracting polynomials worksheet

Part of: Polynomials & identities

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Algebraic expressions · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.(6x + 14) + (2x + 15) = x +
Fill in each blank
Answer:
2.(5x + 14) + (7x + 3) = x +
Fill in each blank
Answer:
3.After simplifying 9x²y − 9xy² + 7x²y + 6xy², the coefficient of xy² is .
Answer:
4.(−5x² + 9x) − (−2x² + 9x) ≡ px² + qx, so p = and q = .
Fill in each blank
Answer:
5.After simplifying 2x²y − 2xy² + 5x²y + 7xy², the coefficient of xy² is .
Answer:
6.(7x² + 4x) − (−5x² + x) ≡ px² + qx, so p = and q = .
Fill in each blank
Answer:
7.(6x + 6) + (3x − 8) − (2x + 5) ≡ px + q, so p = and q = .
Fill in each blank
Answer:

13.If 4x³yⁿ and 8x^my⁶ are like terms, then m + n = .
Working:
Answer:
14.A triangle's sides are (5x + 14) cm, (7x − 13) cm and (9x + 10) cm long. Its perimeter is (x + ) cm.
Fill in each blank
Working:
Answer:
15.Simplify (6x² + 6x) − (3x² − 5x). Put the steps in order.
- A. = 6x² − 3x² + 6x + 5x
- B. Expression = 6x² + 6x − 3x² + 5x
- C. = 3x² + 11x
Write the letters in the right order
Working:
Answer:
16.A polynomial plus 4x² + 6x + 2 gives 8x² + 6x + 5. Written as px² + qx + r, the polynomial has p = , q = and r = .
Fill in each blank
Working:
Answer:
17.A rectangle is (7x + 8) m long and (3x − 6) m wide. Its length is (x + ) m more than its width.
Fill in each blank
Working:
Answer:
18.May meant to take 3x² − 2x + 7 away from a polynomial, but added it instead and got 9x² + 5x + 12. What is the right answer?
- A. 6x² + 2x + 5
- B. 3x² + 9x − 2
- C. 9x² + 9x + 12
- D. 12x² + 3x + 19
Choose the right answer
Working:
Answer:

Show the answers and working

Adding and subtracting polynomials worksheet: Answers and working

1. 8, 29
Combine like terms: 6x + 2x = 8x and 14 + 15 = 29.
2. 12, 17
Combine like terms: 5x + 7x = 12x and 14 + 3 = 17.
3. −3
xy²'s like terms are −9xy² and 6xy²: −9 + 6 = −3. x²y has different indices, so it is not one of them (together those make 16x²y).
4. −3, 0
Taking the bracket away changes every sign: p = (−5) − (−2) = −3, q = (9) − (9) = 0.
5. 5
xy²'s like terms are −2xy² and 7xy²: −2 + 7 = 5. x²y has different indices, so it is not one of them (together those make 7x²y).
6. 12, 3
Taking the bracket away changes every sign: p = (7) − (−5) = 12, q = (4) − (1) = 3.
7. 7, −7
Copy the bracket added; change every sign in the one taken away: p = 6 + 3 − 2 = 7, q = (6) + (−8) − (5) = −7.

8. False
Like terms have the same letters, each to the same index: here x's indices are 2 and 3.
9. D. −2x² − 6x + 3
Remove the brackets: 4x² + 3x + 6 − 6x² − 9x − 3, then combine like terms.
10. A. x² − 2x + 7
Remove the brackets: 2x² + 6x + 17 − x² − 8x − 10, then combine like terms.
11. C. −4x² − 6x + 16
A − B = 5x² − x + 5 − 9x² − 5x + 11; combining like terms gives −4x² − 6x + 16.
12. A. x² − 15x + 26
A − B = 2x² − 9x + 15 − x² − 6x + 11; combining like terms gives x² − 15x + 26.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 9
Like terms have each letter to the same index: m = 3 and n = 6, so m + n = 9.
14. 21, 11
The perimeter is the three sides added: x terms 5 + 7 + 9 = 21, numbers 14 − 13 + 10 = 11.
15. B → A → C
Remove the brackets first (every sign in the one taken away changes), then put like terms together, then combine them.
16. 4, 0, 3
The polynomial = the result − what was added: p = 8 − 4 = 4, q = (6) − (6) = 0, r = (5) − (2) = 3.
17. 4, 14
Length − width = (7x + 8) − (3x − 6) = 7x + 8 − 3x + 6 = 4x + 14. Taking away −6 adds 6.
18. B. 3x² + 9x − 2
The polynomial = the wrong result − (3x² − 2x + 7) = 6x² + 7x + 5; the right answer = that − (3x² − 2x + 7) = 3x² + 9x − 2.

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