The problem asks us to simplify the given algebraic expressions by combining like terms. There are 12 expressions to simplify.

1. Problem Description

The problem asks us to simplify the given algebraic expressions by combining like terms. There are 12 expressions to simplify.

2. Solution Steps

1. $3x + 4y + 7y$

Combine the $y$ terms: $4y + 7y = 11y$

So the simplified expression is $3x + 11y$

2. $4a + 7b - 2a + b$

Combine the $a$ terms: $4a - 2a = 2a$

Combine the $b$ terms: $7b + b = 8b$

So the simplified expression is $2a + 8b$

3. $3x - 2y + 4y$

Combine the $y$ terms: $-2y + 4y = 2y$

So the simplified expression is $3x + 2y$

4. $2x + 3x + 5$

Combine the $x$ terms: $2x + 3x = 5x$

So the simplified expression is $5x + 5$

5. $7 - 3x + 2 + 4x$

Combine the constant terms: $7 + 2 = 9$

Combine the $x$ terms: $-3x + 4x = x$

So the simplified expression is $x + 9$ or $9 + x$

6. $5 - 3y - 6y - 2$

Combine the constant terms: $5 - 2 = 3$

Combine the $y$ terms: $-3y - 6y = -9y$

So the simplified expression is $-9y + 3$ or $3 - 9y$

7. $5x + 2y - 4y - x^2$

Combine the $y$ terms: $2y - 4y = -2y$

So the simplified expression is $5x - 2y - x^2$ or $-x^2 + 5x - 2y$

8. $2x^2 + 3x + 5$

There are no like terms to combine.

So the simplified expression is $2x^2 + 3x + 5$

9. $2x - 7y - 2x - 3y$

Combine the $x$ terms: $2x - 2x = 0$

Combine the $y$ terms: $-7y - 3y = -10y$

So the simplified expression is $-10y$

1

0. $4a + 3a^2 - 2a$

Combine the $a$ terms: $4a - 2a = 2a$

So the simplified expression is $3a^2 + 2a$

1

1. $7a - 7a^2 + 7$

Rearrange to standard form: $-7a^2 + 7a + 7$

1

2. $x^2 + 3x^2 - 4x^2 + 5x$

Combine the $x^2$ terms: $x^2 + 3x^2 - 4x^2 = (1+3-4)x^2 = 0x^2 = 0$

So the simplified expression is $5x$

3. Final Answer

1. $3x + 11y$

2. $2a + 8b$

3. $3x + 2y$

4. $5x + 5$

5. $x + 9$

6. $3 - 9y$

7. $-x^2 + 5x - 2y$

8. $2x^2 + 3x + 5$

9. $-10y$

1

0. $3a^2 + 2a$

1

1. $-7a^2 + 7a + 7$

1

2. $5x$