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Simplifying Algebraic Expressions 2 - 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=multiply

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

 1.   ( - 3w -3 )( 2w ) = 2.   ( 3y )( 6y -4 ) =

Complexity=5, Mode=exponent

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

 1.   ( 7n -2) 1 = 2.   ( 10n -1) 1 =

Complexity=5, Mode=root

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

1.
 25n 4
=
2.
 9x 2
=

Complexity=5

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

1.   ( 10h -3 )( -h 5 ) =
2.
 49y 2
=

Complexity=5, Mode=multiply

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

1( - 3w -3 )( 2w ) =
Solution
 ( - 3w -3 )( 2w ) = -3 • w -3 • 2 • w 1 = ( -3 • 2 )( w -3 • w 1 ) = -6 • w-3 + 1 = - 6w -2
2( 3y )( 6y -4 ) =
Solution
 ( 3y )( 6y -4 ) = 3 • y 1 • 6 • y -4 = ( 3 • 6 )( y 1 • y -4 ) = 18 • y1 + -4 = 18y -3

Complexity=5, Mode=exponent

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

1( 7n -2) 1 =
Solution
Any number to the 1st power is itself.
2( 10n -1) 1 =
Solution
Any number to the 1st power is itself.

Complexity=5, Mode=root

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.

1
 25n 4
=
2
 9x 2
=

Complexity=5

Simplify the following. Expand to the form abc, where a & c are numeric and b is a variable, such as 3x2. Use ^ for exponent, like 3x^2.