Algebraic expressions · Ages 13–14

A monomial times a polynomial 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.

1.7x(5x + 9) = x² + x
Fill in each blank
Answer:
2.6x(2x + 3) = x² + x
Fill in each blank
Answer:
3.After simplifying 6x(4x + 7) − 3x², the coefficient of x² is .
Answer:
4.−x(−3x + 6) ≡ px² + qx, so p = and q = .
Fill in each blank
Answer:
5.After simplifying 5x(6x + 5) − 15x², the coefficient of x² is .
Answer:
6.5x(4x − 6) ≡ px² + qx, so p = and q = .
Fill in each blank
Answer:
7.8x(x + 1) + 4(x² − 3x) ≡ px² + qx, so p = and q = .
Fill in each blank
Answer:

13.Simplify 8x(x − 5) − 2(x² + 5x). Put the steps in order.
- A. = 6x² − 50x
- B. Expression = 8x² − 40x − 2x² − 10x
- C. = 8x² − 2x² − 40x − 10x
Write the letters in the right order
Working:
Answer:
14.A rectangle is 4x cm wide, and its length is 4 cm more than 3 times its width. The length is (x + 4) cm and the area is (x² + x) cm².
Fill in each blank
Working:
Answer:
15.A square board has sides 7x cm long. After a rectangle 6x cm long and 6 cm wide is cut from it, the area left is (49x² − x) cm².
Working:
Answer:
16.A rectangular poster is x cm wide and (8x − 1) cm long. What is its area in cm²?
- A. 8x² − x
- B. 18x − 2
- C. 8x² − 1
- D. 9x − 1
Choose the right answer
Working:
Answer:
17.Simplify 4x(x − 1) − 6x(2x + 6) and write it as px² + qx: p = and q = .
Fill in each blank
Working:
Answer:
18.Chi-keung says: −4x(6x − 2) = −24x² + 8x.
True or false?
Working:
Answer:

Show the answers and working

A monomial times a polynomial worksheet: Answers and working

1. 35, 63
7x times every term inside: 7x × 5x = 35x² and 7x × 9 = 63x.
2. 12, 18
6x times every term inside: 6x × 2x = 12x² and 6x × 3 = 18x.
3. 21
6x × 4x = 24x², then take away 3x²: 24 − 3 = 21.
4. 3, −6
The term outside times every term inside: p = (−1) × (−3) = 3, q = (−1) × (6) = −6. Same signs make a positive, different signs a negative.
5. 15
5x × 6x = 30x², then take away 15x²: 30 − 15 = 15.
6. 20, −30
The term outside times every term inside: p = (5) × (4) = 20, q = (5) × (−6) = −30. Same signs make a positive, different signs a negative.
7. 12, −4
Expand: 8x² + 8x + 4x² − 12x. p = 8 + 4 = 12, q = 8 − 12 = −4.

8. B. 28x⁶
Multiply the coefficients: 4 × 7 = 28; add the indices: 2 + 4 = 6.
9. C. 81x⁶
Multiply the coefficients: 9 × 9 = 81; add the indices: 2 + 4 = 6.
10. D. −16x² + 14x
−2x times each term: (−2x) × 8x = −16x² and (−2x) × (−7) = +14x.
11. False
Coefficients: 5 × 5 = 25; x² × x = x³; y × y⁴ = y⁵, as y alone has index 1.
12. True
Coefficients: 4 × 2 = 8; x² × x = x³; y × y⁵ = y⁶, as y alone has index 1.

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

13. B → C → A
Multiply out the brackets by the distributive law, put like terms together, then combine them.
14. 12, 48, 16
Length = 3 × 4x + 4 = 12x + 4; area = 4x(12x + 4) = 48x² + 16x.
15. 36
The square is (7x)² = 49x²; the cut-out is 6x × 6 = 36x; left: 49x² − 36x.
16. A. 8x² − x
Area = length × width = x(8x − 1) = 8x² − x.
17. −8, −40
4x² − 4x − 12x² − (36)x: p = 4 − 12 = −8, q = −4 − (36) = −40. A minus before the second bracket changes the sign of each term multiplied out.
18. True
(−4x) × (−2) is a negative times a negative, +8x, so −4x(6x − 2) = −24x² + 8x.

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