logo for solving-math-problems.com
leftimage for solving-math-problems.com

Algebra Accelerated

by Rob
(California)











































Simplify the following algebraic expression:

-32a-2(5a-2a)+2-8-2(2a-3b)

Show how to use the PEMDAS order of operations.

Comments for Algebra Accelerated

Click here to add your own comments

Sep 11, 2011
Simplifying Algebraic Expression - PEMDAS
by: Staff


The question:

by Rob
(California)

-32a-2(5a-2a)+2-8-2(2a-3b)


The answer:

-32a - 2(5a - 2a) + 2 – 8 - 2(2a - 3b)


You have submitted an excellent example for illustrating how to use the PEMDAS order of operations.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction

PEMDAS order tells you what to do first, second, . . . etc.


Step 1: you should evaluate the expression inside each set of PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

There are two expressions enclosed in parentheses:

(5a - 2a)

(2a - 3b)


This expression (2a - 3b) cannot be simplified further. For the moment, it will remain (2a - 3b)

This expression (5a - 2a) can be simplified. The two like terms can be combined:

(5a - 2a) = (3a)

After simplifying the expressions inside the parentheses, you original expression now looks like this:

-32a - 2(3a) + 2 – 8 - 2(2a - 3b)



Step 2: evaluate EXPONENTS


PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.


Step 3: MULTIPLICATION


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

There are two places in your expression where you should complete the multiplication now:

- 2(3a)

and

- 2(2a - 3b)


Simplifying - 2(3a)

- 2(3a)

= (-2) * (3a)

= -2 * 3a

= -6a


Simplifying - 2(2a - 3b)

- 2(2a - 3b)

= (-2) * (2a - 3b)

= (-2) * (2a) + (-2) * (-3b)

= -4a + 6b



After completing the multiplication, your expression looks like this:


-32a - 6a + 2 – 8 - 4a + 6b


Step 4: DIVISION


PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

No division is necessary to simplify your expression.

Step 5: evaluate ADDITION & SUBTRACTION

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

You can now combine like terms.

-32a - 6a + 2 - 8 - 4a + 6b

-32a - 6a - 4a + 6b + 2 - 8

(-32a - 6a - 4a) + 6b + (2 - 8)

-42a + 6b + (- 6)

-42a + 6b - 6


The final answer to your question is: -42a + 6b - 6


A step-by-step recap of the entire process looks like this:

-32a - 2(5a - 2a) + 2 – 8 - 2(2a - 3b)

-32a - 2(3a) + 2 – 8 - 2(2a - 3b)

-32a + (-2) * (3a) + 2 - 8 + (-2) * (2a - 3b)

-32a + (-2) * (3a) + 2 - 8 + (-2) * (2a) + (-2) * (-3b)

-32a - 6a + 2 - 8 – 4a + 6b

-32a - 6a - 4a + 6b + 2 - 8

(-32a - 6a - 4a) + 6b + (2 - 8)

-42a + 6b + (- 6)

-42a + 6b - 6





Thanks for writing.

Staff
www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com