Let’s solve each problem step by step. We’ll combine like terms — that means adding or subtracting coefficients of the same power of x (like all the x³ terms, all the x² terms, etc.).
---
1) 6x + 4x² + x³ + 7x – 7
Group like terms:
- x³: only one →
x³
- x²: only one →
4x²
- x: 6x + 7x =
13x
- constant:
–7
Answer:
x³ + 4x² + 13x – 7
---
2) 13x³ + 7x² – 4x³ + 17x² – 20x³ + 11x²
Group like terms:
- x³: 13 – 4 – 20 =
–11x³
- x²: 7 + 17 + 11 =
35x²
Answer:
–11x³ + 35x²
---
3) 11x + 3x² – x³ + 5x
Group like terms:
- x³:
–x³
- x²:
3x²
- x: 11x + 5x =
16x
Answer:
–x³ + 3x² + 16x
---
4) 19x + 6x² – x³ + 3x
Group like terms:
- x³:
–x³
- x²:
6x²
- x: 19x + 3x =
22x
Answer:
–x³ + 6x² + 22x
---
5) (20x³ + 7x² – 5x³) + (25x² – 27x³ + 12x²)
First, remove parentheses and combine:
x³ terms: 20 – 5 – 27 =
–12x³
x² terms: 7 + 25 + 12 =
44x²
Answer:
–12x³ + 44x²
---
6) (8x³ + 6x² – 4x³) + (12x² – 14x³ + 10x²)
Combine:
x³: 8 – 4 – 14 =
–10x³
x²: 6 + 12 + 10 =
28x²
Answer:
–10x³ + 28x²
---
7) 5x³ + 6x² – 3x³ + 8x² – 11x³ + 9x²
x³: 5 – 3 – 11 =
–9x³
x²: 6 + 8 + 9 =
23x²
Answer:
–9x³ + 23x²
---
8) (10x³ + 5x² – 5x³) + (15x² – 15x³ + 10x²)
x³: 10 – 5 – 15 =
–10x³
x²: 5 + 15 + 10 =
30x²
Answer:
–10x³ + 30x²
---
9) (11x³ + 6x² – 4x³) + (15x² – 17x³ + 10x²)
x³: 11 – 4 – 17 =
–10x³
x²: 6 + 15 + 10 =
31x²
Answer:
–10x³ + 31x²
---
10) (9x³ + 2x² – 7x³) + (16x² – 11x³ + 9x²)
x³: 9 – 7 – 11 =
–9x³
x²: 2 + 16 + 9 =
27x²
Answer:
–9x³ + 27x²
---
11) 8x + 2x² – x³ + 5x
x³:
–x³
x²:
2x²
x: 8x + 5x =
13x
Answer:
–x³ + 2x² + 13x
---
Final Answer:
1) x³ + 4x² + 13x – 7
2) –11x³ + 35x²
3) –x³ + 3x² + 16x
4) –x³ + 6x² + 22x
5) –12x³ + 44x²
6) –10x³ + 28x²
7) –9x³ + 23x²
8) –10x³ + 30x²
9) –10x³ + 31x²
10) –9x³ + 27x²
11) –x³ + 2x² + 13x
Parent Tip: Review the logic above to help your child master the concept of simplifying polynomials worksheet.
