To solve the problem, we need to simplify each expression by combining like terms. Let's go through each expression step by step.
---
Expression 1:
$$
3a^2 + 4x^3 - a^2 - 2x^3
$$
- Combine the $a^2$ terms: $3a^2 - a^2 = 2a^2$
- Combine the $x^3$ terms: $4x^3 - 2x^3 = 2x^3$
Simplified expression:
$$
2a^2 + 2x^3
$$
---
Expression 2:
$$
y^2 + 7y^3 + y^2 + 7y^3
$$
- Combine the $y^2$ terms: $y^2 + y^2 = 2y^2$
- Combine the $y^3$ terms: $7y^3 + 7y^3 = 14y^3$
Simplified expression:
$$
2y^2 + 14y^3
$$
---
Expression 3:
$$
3a + 41a - a - 2x^2 + 2a
$$
- Combine the $a$ terms: $3a + 41a - a + 2a = 45a$
- The $-2x^2$ term remains as it is (no like terms to combine with).
Simplified expression:
$$
45a - 2x^2
$$
---
Expression 4:
$$
1b^2 - 4b^2 - b^2 - 2b^2
$$
- Combine all the $b^2$ terms: $1b^2 - 4b^2 - b^2 - 2b^2 = -6b^2$
Simplified expression:
$$
-6b^2
$$
---
Expression 5:
$$
3m^2 + 4m^3 - m^2
$$
- Combine the $m^2$ terms: $3m^2 - m^2 = 2m^2$
- The $4m^3$ term remains as it is (no like terms to combine with).
Simplified expression:
$$
2m^2 + 4m^3
$$
---
Expression 6:
$$
-2d^2 - 6e^3 - 5d^2 - 2e^3 + e^3 + 4a^2
$$
- Combine the $d^2$ terms: $-2d^2 - 5d^2 = -7d^2$
- Combine the $e^3$ terms: $-6e^3 - 2e^3 + e^3 = -7e^3$
- The $4a^2$ term remains as it is (no like terms to combine with).
Simplified expression:
$$
-7d^2 - 7e^3 + 4a^2
$$
---
Expression 7:
$$
5k^2m^3n^6 + 8k^2m^3n^6
$$
- Combine the $k^2m^3n^6$ terms: $5k^2m^3n^6 + 8k^2m^3n^6 = 13k^2m^3n^6$
Simplified expression:
$$
13k^2m^3n^6
$$
---
Expression 8:
$$
15w^2 - 11w^2
$$
- Combine the $w^2$ terms: $15w^2 - 11w^2 = 4w^2$
Simplified expression:
$$
4w^2
$$
---
Expression 9:
$$
3g + 9 - g - 7
$$
- Combine the $g$ terms: $3g - g = 2g$
- Combine the constant terms: $9 - 7 = 2$
Simplified expression:
$$
2g + 2
$$
---
Expression 10:
$$
2s^2 + 6t^3 - 4s^2 - 4s^4 + 2t^3 - s^4 + 2s^4 + 6s^2 - t^3
$$
- Combine the $s^2$ terms: $2s^2 - 4s^2 + 6s^2 = 4s^2$
- Combine the $s^4$ terms: $-4s^4 - s^4 + 2s^4 = -3s^4$
- Combine the $t^3$ terms: $6t^3 + 2t^3 - t^3 = 7t^3$
Simplified expression:
$$
4s^2 - 3s^4 + 7t^3
$$
---
Final Answer:
$$
\boxed{
\begin{aligned}
1. & \ 2a^2 + 2x^3 \\
2. & \ 2y^2 + 14y^3 \\
3. & \ 45a - 2x^2 \\
4. & \ -6b^2 \\
5. & \ 2m^2 + 4m^3 \\
6. & \ -7d^2 - 7e^3 + 4a^2 \\
7. & \ 13k^2m^3n^6 \\
8. & \ 4w^2 \\
9. & \ 2g + 2 \\
10. & \ 4s^2 - 3s^4 + 7t^3
\end{aligned}
}
$$
Parent Tip: Review the logic above to help your child master the concept of adding monomials worksheet.
