Problem 1: Add the polynomials $(4x^2 + 4x + 1) + (4x + 20)$
#### Step-by-Step Solution:
1.
Write down the given polynomials:
\[
(4x^2 + 4x + 1) + (4x + 20)
\]
2.
Remove the parentheses:
\[
4x^2 + 4x + 1 + 4x + 20
\]
3.
Group like terms together:
- Terms with $x^2$: $4x^2$
- Terms with $x$: $4x + 4x$
- Constant terms: $1 + 20$
So, we have:
\[
4x^2 + (4x + 4x) + (1 + 20)
\]
4.
Combine like terms:
- For the $x^2$ term: $4x^2$ (no other $x^2$ terms to combine with)
- For the $x$ terms: $4x + 4x = 8x$
- For the constant terms: $1 + 20 = 21$
Therefore:
\[
4x^2 + 8x + 21
\]
5.
Write the final answer:
\[
\boxed{4x^2 + 8x + 21}
\]
---
Problem 3: Add the polynomials $(5x^3 - 6x + 10) + (x^3 + 10x - 9)$
#### Step-by-Step Solution:
1.
Write down the given polynomials:
\[
(5x^3 - 6x + 10) + (x^3 + 10x - 9)
\]
2.
Remove the parentheses:
\[
5x^3 - 6x + 10 + x^3 + 10x - 9
\]
3.
Group like terms together:
- Terms with $x^3$: $5x^3 + x^3$
- Terms with $x$: $-6x + 10x$
- Constant terms: $10 - 9$
So, we have:
\[
(5x^3 + x^3) + (-6x + 10x) + (10 - 9)
\]
4.
Combine like terms:
- For the $x^3$ terms: $5x^3 + x^3 = 6x^3$
- For the $x$ terms: $-6x + 10x = 4x$
- For the constant terms: $10 - 9 = 1$
Therefore:
\[
6x^3 + 4x + 1
\]
5.
Write the final answer:
\[
\boxed{6x^3 + 4x + 1}
\]
---
Final Answers:
1. $(4x^2 + 4x + 1) + (4x + 20) = \boxed{4x^2 + 8x + 21}$
3. $(5x^3 - 6x + 10) + (x^3 + 10x - 9) = \boxed{6x^3 + 4x + 1}$
Parent Tip: Review the logic above to help your child master the concept of adding polynomials worksheet answers.
