Equivalent expressions with negative numbers and the distributive property

The  exercise appears under the 7th grade (U.S.) Math Mission. This exercise applies the distributive property to algebraic expressions and negative numbers.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the equivalent expressions: This problem provides a given algebraic expression and two possibly equivalent expressions. The student is to select which, if either, of the proposed expressions are actually equivalent upon simplification.Eewnnatdp1.png

Strategies
Knowledge of the distributive property and comfort with operations involving negative numbers are encouraged to ensure success on this exercise.
 * 1) Not all of the expressions are fully simplified, it is important to pay attention to this when selecting equivalent expressions.
 * 2) The expressions are linear, so concentrating on the variable and the constant separately can increase efficiency.
 * 3) Plugging in a number for the variable may slightly increase efficiency, but will not always provide correct answers. It can be used for eliminating possible answers.
 * 4) The distributive property states that $$a(b+c)=ab+ac$$

Real-life Applications

 * 1) An ability to manipulate expressions into alternative but equivalent forms is useful in higher algebra courses as well as standardized tests like the SAT.