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having trouble-combining variables











































5x2x^2-7x+9-(2x^3+4x^2)/2x^2

use PEMDAS order to simplify this expression.

Simplify in the following order: parentheses, exponents, multiplication, division, addition, subtraction.

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May 19, 2010
Combining Variables
by: Staff

Combining Variables


The problem: simplify the following expression

5x2x^2-7x+9-(2x^3+4x^2)/2x^2

The solution


Notes

The 5x at the beginning of your expression is not bold faced, even though the remainder of the expression is written bold faced text.

Because of this difference, I cannot be sure whether the 5x at the beginning of your expression means 5 times the variable x, or 5 times 2x.

I will simplify your expression both ways.




Case I: If 5x means 5 times the variable x


Step 1 - Write out the original problem:

5x2x^2 - 7x + 9 -(2x^3 + 4x^2)/2x^2


NOTE - It is important to use PEMDAS order to simplify this expression. Simplify in the following order: parentheses, exponents, multiplication, division, addition, subtraction.



Step 2 - Simplify the expression which appears inside the parentheses

(2x^3 + 4x^2) = this expression cannot be simplified


Step 3 - Now consider the parentheses and the division problem together

(2x^3 + 4x^2)/2x^2


Step 4 - factor the expression in the parentheses

(2x^3 + 4x^2)/2x^2 = 2x^2(x + 2)/ 2x^2

Step 5 - the factor 2x^2 appears in both the numerator and the denominator ? they cancel one another

2x^2(x + 2)/ 2x^2= (x + 2)

Step 6 - substitute the result back into the original expression

5x2x^2-7x+9-(x + 2)

Step 7 - multiply the 1st term

5x2x^2 = 10x^3

Step 8 - substitute the result back into the expression. The original expression now appears as follows:

10x^3 - 7x + 9 -(x + 2)

Step 9 - since the last term in the expression is a parentheses preceded by a minus sign, multiply each term in the expression by a minus 1. The original expression now appears as follows:

-(x + 2) = -x -2

Step 10 - substitute the result back into the expression. The original expression now appears as follows:

10x^3-7x+9-x -2

Step 11 - group like terms together as follows:

10x^3 - 7x - x + 9 -2

Step 12 - combine like terms:

10x^3 - 8x + 7

You are finished. The final answer is: 10x^3 - 8x + 7


Case II: If 5x simply means 5 times (not 5 times the variable x)

In this case the first term changes to: 10x^2 (not 10x^3)

You are finished. The final answer is: 10x^2 - 8x + 7



Thanks for writing.


Staff
www.solving-math-problems.com



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