To find the difference of the polynomials, we first need to combine like terms. Let’s organize the polynomials Samuel is working with:
- 15x²
- 11y²
- 8x
- -7x²
- -5y²
- -2x
- -x²
- -6y²
- -6x
Now we can group them:
- For x² terms: 15x² – 7x² – x² = 15x² – 8x² = 7x²
- For y² terms: 11y² – 5y² – 6y² = 11y² – 11y² = 0
- For x terms: 8x – 2x – 6x = 8x – 8x = 0
After combining these, we get:
- 7x²
- 0 for y²
- 0 for x
Therefore, the final expression is simply:
7x²
In Samuel’s solution, the key value missing was the recognition that the y² and x terms cancel out to zero, leaving only the x² term. Thus, the complete final polynomial represents just the x² component: 7x².