Answer :
Certainly! Let's go through the process of simplifying each expression step-by-step:
### First Expression: [tex]\( 2m + 5m + m + 10m - 3m \)[/tex]
1. Combine like terms by adding or subtracting the coefficients of [tex]\( m \)[/tex]:
[tex]\[ 2m + 5m + m + 10m - 3m \][/tex]
2. Add and subtract the coefficients:
[tex]\[ (2 + 5 + 1 + 10 - 3)m \][/tex]
3. Simplify inside the parentheses:
[tex]\[ 15m \][/tex]
So, the simplified form of the first expression is:
[tex]\[ 15m \][/tex]
### Second Expression: [tex]\( 4a^2 + 2a^2 + 3b^3 + b^3 + 7c^5 - 5c^5 \)[/tex]
1. Combine like terms by grouping the terms with the same variables and exponents:
[tex]\[ 4a^2 + 2a^2 + 3b^3 + b^3 + 7c^5 - 5c^5 \][/tex]
2. Add the coefficients of [tex]\( a^2 \)[/tex]:
[tex]\[ (4 + 2)a^2 = 6a^2 \][/tex]
3. Add the coefficients of [tex]\( b^3 \)[/tex]:
[tex]\[ (3 + 1)b^3 = 4b^3 \][/tex]
4. Subtract the coefficients of [tex]\( c^5 \)[/tex]:
[tex]\[ (7 - 5)c^5 = 2c^5 \][/tex]
So, the simplified form of the second expression is:
[tex]\[ 6a^2 + 4b^3 + 2c^5 \][/tex]
### Third Expression: [tex]\( x + 3y + x + 2x - y + 2z \)[/tex]
1. Combine like terms by grouping the terms with the same variables:
[tex]\[ x + 3y + x + 2x - y + 2z \][/tex]
2. Add the coefficients of [tex]\( x \)[/tex]:
[tex]\[ (1 + 1 + 2)x = 4x \][/tex]
3. Add and subtract the coefficients of [tex]\( y \)[/tex]:
[tex]\[ (3 - 1)y = 2y \][/tex]
4. [tex]\( z \)[/tex] is already grouped:
[tex]\[ 2z \][/tex]
So, the simplified form of the third expression is:
[tex]\[ 4x + 2y + 2z \][/tex]
### Final Simplified Forms:
1. The first expression simplifies to: [tex]\( 15m \)[/tex]
2. The second expression simplifies to: [tex]\( 6a^2 + 4b^3 + 2c^5 \)[/tex]
3. The third expression simplifies to: [tex]\( 4x + 2y + 2z \)[/tex]
Combining all these together, we have:
- [tex]\( 15m \)[/tex]
- [tex]\( 6a^2 + 4b^3 + 2c^5 \)[/tex]
- [tex]\( 4x + 2y + 2z \)[/tex]
### First Expression: [tex]\( 2m + 5m + m + 10m - 3m \)[/tex]
1. Combine like terms by adding or subtracting the coefficients of [tex]\( m \)[/tex]:
[tex]\[ 2m + 5m + m + 10m - 3m \][/tex]
2. Add and subtract the coefficients:
[tex]\[ (2 + 5 + 1 + 10 - 3)m \][/tex]
3. Simplify inside the parentheses:
[tex]\[ 15m \][/tex]
So, the simplified form of the first expression is:
[tex]\[ 15m \][/tex]
### Second Expression: [tex]\( 4a^2 + 2a^2 + 3b^3 + b^3 + 7c^5 - 5c^5 \)[/tex]
1. Combine like terms by grouping the terms with the same variables and exponents:
[tex]\[ 4a^2 + 2a^2 + 3b^3 + b^3 + 7c^5 - 5c^5 \][/tex]
2. Add the coefficients of [tex]\( a^2 \)[/tex]:
[tex]\[ (4 + 2)a^2 = 6a^2 \][/tex]
3. Add the coefficients of [tex]\( b^3 \)[/tex]:
[tex]\[ (3 + 1)b^3 = 4b^3 \][/tex]
4. Subtract the coefficients of [tex]\( c^5 \)[/tex]:
[tex]\[ (7 - 5)c^5 = 2c^5 \][/tex]
So, the simplified form of the second expression is:
[tex]\[ 6a^2 + 4b^3 + 2c^5 \][/tex]
### Third Expression: [tex]\( x + 3y + x + 2x - y + 2z \)[/tex]
1. Combine like terms by grouping the terms with the same variables:
[tex]\[ x + 3y + x + 2x - y + 2z \][/tex]
2. Add the coefficients of [tex]\( x \)[/tex]:
[tex]\[ (1 + 1 + 2)x = 4x \][/tex]
3. Add and subtract the coefficients of [tex]\( y \)[/tex]:
[tex]\[ (3 - 1)y = 2y \][/tex]
4. [tex]\( z \)[/tex] is already grouped:
[tex]\[ 2z \][/tex]
So, the simplified form of the third expression is:
[tex]\[ 4x + 2y + 2z \][/tex]
### Final Simplified Forms:
1. The first expression simplifies to: [tex]\( 15m \)[/tex]
2. The second expression simplifies to: [tex]\( 6a^2 + 4b^3 + 2c^5 \)[/tex]
3. The third expression simplifies to: [tex]\( 4x + 2y + 2z \)[/tex]
Combining all these together, we have:
- [tex]\( 15m \)[/tex]
- [tex]\( 6a^2 + 4b^3 + 2c^5 \)[/tex]
- [tex]\( 4x + 2y + 2z \)[/tex]
