Math Practice Problems - Simplifying Algebraic Expressions

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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=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).

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).

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).

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).

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).

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).

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).

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).

Answers

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).

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).

#	Problem	Correct Answer	Your Answer
1	^-1 - 1 + 2 + x - 7	Simplified:
Solution ^-1 + ^-1 + 2 = 0

#	Problem	Correct Answer	Your Answer
2	2x + 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).

#	Problem	Correct Answer	Your Answer
1	5y + 4 + 3x + 5y + 4y	Simplified:
Solution 5y + 5y + 4y = 14y

#	Problem	Correct Answer	Your Answer
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).

#	Problem	Correct Answer	Your Answer
1	-y + 4x² + 4 - 4x² + 1 - 5y²	Simplified:
Solution 4x² + ^-4x² = 0x² 0x² = 0 4 + 1 = 5

#	Problem	Correct Answer	Your Answer
2	7 + 5x² - 2x + 3x + x² + 4x²	Simplified:
Solution 5x² + x² + 4x² = 10x² ^-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).

#	Problem	Correct Answer	Your Answer
1	^-2x² - 5y² - 5y² + 4y - 3x + 5x + 2	Simplified:
Solution ^-5y² + ^-5y² = ^-10y² ^-3x + 5x = 2x

#	Problem	Correct Answer	Your Answer
2	5y² + 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).

Problem

Correct Answer

Your Answer

-(^-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

Problem

Correct Answer

Your Answer

-(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).

Problem

Correct Answer

Your Answer

-(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

Problem

Correct Answer

Your Answer

-(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).

Problem

Correct Answer

Your Answer

^-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

Problem

Correct Answer

Your Answer

-(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).

Problem

Correct Answer

Your Answer

^-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

Problem

Correct Answer

Your Answer

-(^-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

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