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## Simplifying Algebraic Expressions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=3, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   - 5x - 5x + 2 Simplified: 2.   7 - 5x + 5x Simplified:

### Complexity=5, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   - 1 - 1 + 2 + x - 7 Simplified: 2.   2x + 7 - 3x + 5x + x Simplified:

### Complexity=5, Mode=two-vars

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   5y + 4 + 3x + 5y + 4y Simplified: 2.   - 4y + 4y - 3x - 3y - 2 Simplified:

### Complexity=6, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   -y + 4x 2 + 4 - 4x 2 + 1 - 5y 2 Simplified: 2.   7 + 5x 2 - 2x + 3x + x 2 + 4x 2 Simplified:

### Complexity=7, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   - 2x 2 - 5y 2 - 5y 2 + 4y - 3x + 5x + 2 Simplified: 2.   5y 2 + 2 - 2x + 5 + 7 + 3y - 7 Simplified:

### Complexity=2, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   -(- 4y + 3) - (- 2x - 6) Simplified: 2.   -(2 + 4x) - (4y - 5) Simplified:

### Complexity=3, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   -(5y + 2x) - 2(6 - 5) - (-y - 6) Simplified: 2.   -(2y - 7) + 1(- 3x - 7) - (- 5x - 7) Simplified:

### Complexity=4, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   - 3(- 4y - 2x) - (2x + 4y) - 4(- 5x + 3x) - (4y + 5) Simplified: 2.   -(x + 7) + 1(4y + 5y) + 3(4x - 5) - (-y - 3) Simplified:

### Complexity=5, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

 1.   - 3(4y + 8) - 4(4x + 8) - (4y + 1) - (- 3x + x) - 4(-x + x) Simplified: 2.   -(- 2x - 5y) - (- 2y - 4y) - 3(4x - 5y) - (-x - 4x) - (- 3y - 4) Simplified:

### Complexity=3, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1- 5x - 5x + 2
Simplified:
Solution
- 5x + - 5x = - 10x
27 - 5x + 5x
Simplified:
Solution
- 5x + 5x = 0x
0x = 0

### Complexity=5, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1- 1 - 1 + 2 + x - 7
Simplified:
Solution
- 1 + - 1 + 2 = 0
22x + 7 - 3x + 5x + x
Simplified:
Solution
2x + - 3x + 5x + x = 5x

### Complexity=5, Mode=two-vars

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

15y + 4 + 3x + 5y + 4y
Simplified:
Solution
5y + 5y + 4y = 14y
2- 4y + 4y - 3x - 3y - 2
Simplified:
Solution
- 4y + 4y = 0y
0y = 0

### Complexity=6, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1-y + 4x 2 + 4 - 4x 2 + 1 - 5y 2
Simplified:
Solution
4x 2 + - 4x 2 = 0x 2
0x 2 = 0
4 + 1 = 5
27 + 5x 2 - 2x + 3x + x 2 + 4x 2
Simplified:
Solution
5x 2 + x 2 + 4x 2 = 10x 2
- 2x + 3x = 1x

### Complexity=7, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1- 2x 2 - 5y 2 - 5y 2 + 4y - 3x + 5x + 2
Simplified:
Solution
- 5y 2 + - 5y 2 = - 10y 2
- 3x + 5x = 2x
25y 2 + 2 - 2x + 5 + 7 + 3y - 7
Simplified:
Solution
2 + 5 + 7 = 14
14 + - 7 = 7

### Complexity=2, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1-(- 4y + 3) - (- 2x - 6)
Simplified:
Solution
Apply the distributive property to each term.
-(- 4y + 3) → 4y - 3
-(- 2x - 6) → 2x + 6

Now combine like terms
- 3 + 6 = 3

Answer: 2x + 4y + 3

2-(2 + 4x) - (4y - 5)
Simplified:
Solution
Apply the distributive property to each term.
-(2 + 4x) → - 2 - 4x
-(4y - 5) → - 4y + 5

Now combine like terms
- 2 + 5 = 3

Answer: - 4x - 4y + 3

### Complexity=3, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1-(5y + 2x) - 2(6 - 5) - (-y - 6)
Simplified:
Solution
Apply the distributive property to each term.
-(5y + 2x) → - 5y - 2x
- 2(- 5 + 6) → - 2
-(- 6 - y) → 6 + y

Now combine like terms
- 5y + y = - 4y
- 2 + 6 = 4

Answer: - 2x - 4y + 4

2-(2y - 7) + 1(- 3x - 7) - (- 5x - 7)
Simplified:
Solution
Apply the distributive property to each term.
-(2y - 7) → - 2y + 7
1(- 7 - 3x) → - 7 - 3x
-(- 5x - 7) → 5x + 7

Now combine like terms
7 + - 7 + 7 = 7
- 3x + 5x = 2x

Answer: 2x - 2y + 7

### Complexity=4, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1- 3(- 4y - 2x) - (2x + 4y) - 4(- 5x + 3x) - (4y + 5)
Simplified:
Solution
Apply the distributive property to each term.
- 3(- 4y - 2x) → 12y + 6x
-(4y + 2x) → - 4y - 2x
- 4(- 5x + 3x) → 8x
-(5 + 4y) → - 5 - 4y

Now combine like terms
12y + - 4y + - 4y = 4y
6x + - 2x + 8x = 12x

Answer: 12x + 4y - 5

2-(x + 7) + 1(4y + 5y) + 3(4x - 5) - (-y - 3)
Simplified:
Solution
Apply the distributive property to each term.
-(x + 7) → -x - 7
1(4y + 5y) → 9y
3(- 5 + 4x) → - 15 + 12x
-(- 3 - y) → 3 + y

Now combine like terms
-x + 12x = 11x
- 7 + - 15 + 3 = - 19
9y + y = 10y

Answer: 11x + 10y - 19

### Complexity=5, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude.
Examples:   3x + y - 3,   2x + y2 - 4y + 4.
For   x2,   type   x^2.
Example:   x2 - 2x + 3   (type as:   x^2 - 2x + 3).

1- 3(4y + 8) - 4(4x + 8) - (4y + 1) - (- 3x + x) - 4(-x + x)
Simplified:
Solution
Apply the distributive property to each term.
- 3(4y + 8) → - 12y - 24
- 4(8 + 4x) → - 32 - 16x
-(1 + 4y) → - 1 - 4y
-(x - 3x) → 2x
- 4(-x + x) → 0

Now combine like terms
- 12y + - 4y = - 16y
- 24 + - 32 + - 1 = - 57
- 16x + 2x = - 14x

Answer: - 14x - 16y - 57

2-(- 2x - 5y) - (- 2y - 4y) - 3(4x - 5y) - (-x - 4x) - (- 3y - 4)
Simplified:
Solution
Apply the distributive property to each term.
-(- 2x - 5y) → 2x + 5y
-(- 2y - 4y) → 6y
- 3(4x - 5y) → - 12x + 15y
-(-x - 4x) → 5x
-(- 3y - 4) → 3y + 4

Now combine like terms
2x + - 12x + 5x = - 5x
5y + 6y + 15y + 3y = 29y

Answer: - 5x + 29y + 4   