To solve the problems in the image, we need to simplify each expression by combining like terms. Let's go through each problem step by step.
6-Point Problems
1.
$ 2x - 2x^2 $
- This expression cannot be simplified further because the terms are not like terms.
-
Answer: $ 2x - 2x^2 $
2.
$ 4x^2 + 10x $
- This expression cannot be simplified further because the terms are not like terms.
-
Answer: $ 4x^2 + 10x $
3.
$ 15x^3 + 4x^3 $
- Combine like terms: $ 15x^3 + 4x^3 = 19x^3 $
-
Answer: $ 19x^3 $
4.
$ 5x^2 + 45x $
- This expression cannot be simplified further because the terms are not like terms.
-
Answer: $ 5x^2 + 45x $
5.
$ 8x^4 - 2x $
- This expression cannot be simplified further because the terms are not like terms.
-
Answer: $ 8x^4 - 2x $
6.
$ 25x^4 - 21x^4 $
- Combine like terms: $ 25x^4 - 21x^4 = 4x^4 $
-
Answer: $ 4x^4 $
8-Point Problems
1.
$ 3x^2 - 27x - 36 $
- This expression cannot be simplified further because the terms are not like terms.
-
Answer: $ 3x^2 - 27x - 36 $
2.
$ 18x^2 + 114x - 84 $
- This expression cannot be simplified further because the terms are not like terms.
-
Answer: $ 18x^2 + 114x - 84 $
3.
$ 24x^4 + 116x^4 - 16x^4 $
- Combine like terms: $ 24x^4 + 116x^4 - 16x^4 = 124x^4 $
-
Answer: $ 124x^4 $
4.
$ -21x^2 + 28x^2 $
- Combine like terms: $ -21x^2 + 28x^2 = 7x^2 $
-
Answer: $ 7x^2 $
5.
$ 2x^2 - 22x + 56x^2 $
- Combine like terms: $ 2x^2 + 56x^2 - 22x = 58x^2 - 22x $
-
Answer: $ 58x^2 - 22x $
6.
$ -21x^2 + 27 + 3x^2 - 12x $
- Combine like terms: $ -21x^2 + 3x^2 - 12x + 27 = -18x^2 - 12x + 27 $
-
Answer: $ -18x^2 - 12x + 27 $
10-Point Problems
1.
$ 35x^4 - 35x^4 + 250x^4 $
- Combine like terms: $ 35x^4 - 35x^4 + 250x^4 = 250x^4 $
-
Answer: $ 250x^4 $
2.
$ -90x^3 + 95x^3 + 85x^3 - 100x^3 $
- Combine like terms: $ -90x^3 + 95x^3 + 85x^3 - 100x^3 = (-90 + 95 + 85 - 100)x^3 = 90x^3 $
-
Answer: $ 90x^3 $
3.
$ 130x^3 + 60x^3 + 60x^3 + 100x^3 $
- Combine like terms: $ 130x^3 + 60x^3 + 60x^3 + 100x^3 = (130 + 60 + 60 + 100)x^3 = 350x^3 $
-
Answer: $ 350x^3 $
4.
$ -21x^3 + 27x^3 + 2x^3 $
- Combine like terms: $ -21x^3 + 27x^3 + 2x^3 = (-21 + 27 + 2)x^3 = 8x^3 $
-
Answer: $ 8x^3 $
5.
$ 10m^3s^2 - 12m^3s^2 + 24m^3s^2 $
- Combine like terms: $ 10m^3s^2 - 12m^3s^2 + 24m^3s^2 = (10 - 12 + 24)m^3s^2 = 22m^3s^2 $
-
Answer: $ 22m^3s^2 $
Final Answers
\[
\boxed{
\begin{array}{l}
\text{6-Point Problems:} \\
1. \ 2x - 2x^2 \\
2. \ 4x^2 + 10x \\
3. \ 19x^3 \\
4. \ 5x^2 + 45x \\
5. \ 8x^4 - 2x \\
6. \ 4x^4 \\
\\
\text{8-Point Problems:} \\
1. \ 3x^2 - 27x - 36 \\
2. \ 18x^2 + 114x - 84 \\
3. \ 124x^4 \\
4. \ 7x^2 \\
5. \ 58x^2 - 22x \\
6. \ -18x^2 - 12x + 27 \\
\\
\text{10-Point Problems:} \\
1. \ 250x^4 \\
2. \ 90x^3 \\
3. \ 350x^3 \\
4. \ 8x^3 \\
5. \ 22m^3s^2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of greatest common factor factoring worksheet.
