Topic 2: Polynomials
Combine like terms to simplify polynomials.
1. Rewrite using the distributive property: –3(y – 4)
2. Simplify:
7x + y – 2y – 10x
Given x = –2, y = 3, z = –5 Find the value:
3. x + y – z
4. –𝑥 2 y + 𝑧 2
Simplify:
5. (3y – 7) + (–9 – 5y)
6. (𝑥 2 – 5x + 2) – (3𝑥 2 – 3x + 5)
Use the distributive property:
7. x(3 – x)
8. –2(3𝑏 2 – 8b + 7)
9. Multiply (3𝑥 − 1)2
10. Multiply (𝑦 2+ 7)(𝑦 2 − 2)
Write the answer using the appropriate product pattern
11. (2a + 3)(2a + 3)
1
1
12. (4x – 2)( 4x + 2)
Factor:
13. 3𝑥 3 𝑦 − 2𝑥 2 𝑦 4
14. 4𝑥 2 − 21𝑥 + 5
15. 6𝑥 2 − 5𝑥 − 6
ANSWERS:
1. –3y + 12
2. –3x – y
3. 6
4. 13
5. –2y – 16
6. −2𝑥 2 – 2x – 3
7. 3𝑥 - 𝑥 2
8. −6𝑏 2 + 16b – 14
9. 9𝑥 2 – 6x + 1
10. 𝑦 4 + 5𝑦 2 – 14
11. 4𝑎2 +12a + 9
1
12. 16𝑥 2 – 4
13. 𝑥 2 𝑦(3𝑥 − 2𝑦 3 )
14. (4𝑥 − 1)(𝑥 − 5)
15. (2𝑥 − 3)(3𝑥 + 2)
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