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2^a(a-5) +4(a-5) This is the first example that will be used. The variable a is used. This particular example has a coefficient of two.

Step 1:

The distributive property can be utilized to multiply 2a by everything inside of the parenthesis (a-5 in this case) resulting in:

2a^2-10a

Step 2:

The distributive property is used once again to multiply 4 by everything in the parenthesis (a-5 again) resulting in:

4a-20

These two steps demonstrate how the distributive property is used in an effort to remove parenthesis along with making the problem much smaller, less confusing, and easier to work with.

Step 3:

The next step involved should be to put the results from the following two steps together to form one expression:

2a^2-10a+4a-20

Step 4:

The final step involved in this particular example is to simplify the expression even further using a concept known as adding like terms. What this means is that variables are matched and sometimes added or subtracted along with whole numbers to get an expression that can no longer be simplified or broken down. For this example we receive a final expression of:

2a^2-6a-20 this particular expression is simplified and can no longer be broken down any further.

Example 2:

2w-3 +3(w-4) -5(w-6) This is our next example and shows that mathematics and algebra can look even more confusing when compared to the previous example. Distributive property is used to remove parenthesis resulting in:

2w -3 +3w -12 -5w +30 Terms are matched and added together (adding like terms and coefficients) resulting in:

5w -3 -12 -5w +30 which can be simplified even further one last time resulting in:

-15 +30 or 15

Example 3: 0.05(0.3m +35n) -0.8 (-0.09n -22m) This particular example may look like the most complicated out of the previous examples but in fact becomes one of the easiest to solve by remembering the definitions and components utilized in the previous examples. Many people may be inclined to believe that extra steps may be involved when dealing with decimal numbers when in fact; the same exact steps are used.

Distributive property removing parenthesis:

0.015m+1.75n+0.072n+17.6m

Adding Like terms and simplification:

17.615m + 1.822n<<simplest form cannot be broken down any further. In conclusion, mathematics and algebra can at times look very overwhelming and confusing causing many people to become frustrated or to give up. With the basic understanding of key mathematical components and definitions these rather lengthy and seemingly large equations become much smaller and easier to work with. By using distributive properties, one can remove confusing parenthesis. One can then add like terms to shorten the problem and then finally simplify the expression into its smallest and simplest form.…...

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