# 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.

### Comments for having trouble-combining variables

 May 19, 2010 Combining Variables by: Staff Combining Variables The problem: simplify the following expression 5x2x^2-7x+9-(2x^3+4x^2)/2x^2The solutionNotes 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 xStep 1 - Write out the original problem: 5x2x^2 - 7x + 9 -(2x^3 + 4x^2)/2x^2NOTE - 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 simplifiedStep 3 - Now consider the parentheses and the division problem together (2x^3 + 4x^2)/2x^2Step 4 - factor the expression in the parentheses (2x^3 + 4x^2)/2x^2 = 2x^2(x + 2)/ 2x^2Step 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^3Step 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 -2Step 10 - substitute the result back into the expression. The original expression now appears as follows: 10x^3-7x+9-x -2Step 11 - group like terms together as follows: 10x^3 - 7x - x + 9 -2Step 12 - combine like terms: 10x^3 - 8x + 7You are finished. The final answer is: 10x^3 - 8x + 7Case 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 + 7Thanks for writing.Staff www.solving-math-problems.com