Math Practice Problems - Simplifying Algebraic Expressions

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. For x², type x^2. Sample Answers: 3x + y - 3, 2x - 4y + 4, x - y² - 2y + 3 (type as: x - y^2 - 2y + 3)

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

2. ^-5x + 3 - 4x
Simplified:

Complexity=5, Mode=one-var

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

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

2. -x + 6 - 3x - 2x + 7
Simplified:

Complexity=5, Mode=two-vars

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

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

2. ^-2x - 7 - 5x + 8 + y
Simplified:

Complexity=6, Mode=with-exp

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

1. ^-5y² - 3x + 4y² + y - 4 - 3
Simplified:

2. 3x² + 3y - y² + 5y - y² - 5x
Simplified:

Complexity=7, Mode=with-exp

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

1. 2y² + 4 - 7 + 3x - 4y - 3y + 4y
Simplified:

2. 4x² + x² + 4y² + 4y + 7 + 3x + 2
Simplified:

Complexity=2, Mode=with-parens

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

1. -(1 + 3y) + 2(2y - 3)
Simplified:

2. -(5y - 8) - 2(6 + 3)
Simplified:

Complexity=3, Mode=with-parens

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

1. 1(^-2y + 3x) - 2(2 - 5) - 2(8 + 7)
Simplified:

2. -(5 + 6) - (3x + 3y) - 4(^-6 - 7)
Simplified:

Complexity=4, Mode=with-parens

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

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

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

Complexity=5, Mode=with-parens

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

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

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

Answers

Complexity=3, Mode=one-var

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

#	Problem	Correct Answer	Your Answer
1	^-7 + 5x - 2	Simplified:
Solution ^-7 + ^-2 = ^-9

#	Problem	Correct Answer	Your Answer
2	^-5x + 3 - 4x	Simplified:
Solution ^-5x + ^-4x = ^-9x

Complexity=5, Mode=one-var

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

#	Problem	Correct Answer	Your Answer
1	^-3x + 3x - 2 + 5x + 4	Simplified:
Solution ^-3x + 3x + 5x = 5x ^-2 + 4 = 2

#	Problem	Correct Answer	Your Answer
2	-x + 6 - 3x - 2x + 7	Simplified:
Solution -x + ^-3x + ^-2x = ^-6x 6 + 7 = 13

Complexity=5, Mode=two-vars

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

#	Problem	Correct Answer	Your Answer
1	x - 4 - x - 5x + 3y	Simplified:
Solution x + -x + ^-5x = ^-5x

#	Problem	Correct Answer	Your Answer
2	^-2x - 7 - 5x + 8 + y	Simplified:
Solution ^-2x + ^-5x = ^-7x ^-7 + 8 = 1

Complexity=6, Mode=with-exp

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

#	Problem	Correct Answer	Your Answer
1	^-5y² - 3x + 4y² + y - 4 - 3	Simplified:
Solution ^-5y² + 4y² = -y² ^-4 + ^-3 = ^-7

#	Problem	Correct Answer	Your Answer
2	3x² + 3y - y² + 5y - y² - 5x	Simplified:
Solution 3y + 5y = 8y -y² + -y² = ^-2y²

Complexity=7, Mode=with-exp

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

#	Problem	Correct Answer	Your Answer
1	2y² + 4 - 7 + 3x - 4y - 3y + 4y	Simplified:
Solution 4 + ^-7 = ^-3 ^-4y + ^-3y + 4y = ^-3y

#	Problem	Correct Answer	Your Answer
2	4x² + x² + 4y² + 4y + 7 + 3x + 2	Simplified:
Solution 4x² + x² = 5x² 7 + 2 = 9

Complexity=2, Mode=with-parens

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

Problem

Correct Answer

Your Answer

-(1 + 3y) + 2(2y - 3)

Simplified:

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

Now combine like terms
^-1 + ^-6 = ^-7
^-3y + 4y = 1y

Answer: y - 7

Problem

Correct Answer

Your Answer

-(5y - 8) - 2(6 + 3)

Simplified:

Solution
Apply the distributive property to each term.
-(5y - 8) → ^-5y + 8
^-2(3 + 6) → ^-18

Now combine like terms
8 + ^-18 = ^-10

Answer: ^-5y - 10

Complexity=3, Mode=with-parens

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

Problem

Correct Answer

Your Answer

1(^-2y + 3x) - 2(2 - 5) - 2(8 + 7)

Simplified:

Solution
Apply the distributive property to each term.
1(^-2y + 3x) → ^-2y + 3x
^-2(^-5 + 2) → 6
^-2(7 + 8) → ^-30

Now combine like terms
6 + ^-30 = ^-24

Answer: 3x - 2y - 24

Problem

Correct Answer

Your Answer

-(5 + 6) - (3x + 3y) - 4(^-6 - 7)

Simplified:

Solution
Apply the distributive property to each term.
-(5 + 6) → ^-11
-(3y + 3x) → ^-3y - 3x
^-4(^-7 - 6) → 52

Now combine like terms
^-11 + 52 = 41

Answer: ^-3x - 3y + 41

Complexity=4, Mode=with-parens

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

Problem

Correct Answer

Your Answer

-(5 - 4y) - (^-3y - 2) - (^-5y + 5) - 3(^-4x - 2)

Simplified:

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

Now combine like terms
^-5 + 2 + ^-5 + 6 = ^-2
4y + 3y + 5y = 12y

Answer: 12x + 12y - 2

Problem

Correct Answer

Your Answer

2(^-4y + 2y) - (5x - 2y) - (7 - 3) - (2x - x)

Simplified:

Solution
Apply the distributive property to each term.
2(^-4y + 2y) → ^-4y
-(^-2y + 5x) → 2y - 5x
-(^-3 + 7) → ^-4
-(2x - x) → -x

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

Answer: ^-6x - 2y - 4

Complexity=5, Mode=with-parens

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

Problem

Correct Answer

Your Answer

3(5y - 4) - (^-4x - y) + 1(2x + 1) - (4y - 4y) + 1(-x - 4y)

Simplified:

Solution
Apply the distributive property to each term.
3(5y - 4) → 15y - 12
-(^-4x - y) → 4x + y
1(1 + 2x) → 1 + 2x
-(4y - 4y) → 0
1(-x - 4y) → -x - 4y

Now combine like terms
15y + y + ^-4y = 12y
^-12 + 1 = ^-11
4x + 2x + -x = 5x

Answer: 5x + 12y - 11

Problem

Correct Answer

Your Answer

^-4(-y - 5x) + 1(2y - 2y) - 2(^-5x + 3) + 4(^-4x - 3) - (3 + 3)

Simplified:

Solution
Apply the distributive property to each term.
^-4(-y - 5x) → 4y + 20x
1(2y - 2y) → 0
^-2(3 - 5x) → ^-6 + 10x
4(^-4x - 3) → ^-16x - 12
-(3 + 3) → ^-6

Now combine like terms
20x + 10x + ^-16x = 14x
^-6 + ^-12 + ^-6 = ^-24

Answer: 14x + 4y - 24

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