Algebraic Expressions2

Adding Polynomials

      Adding polynomials is just a matter of combining like terms, with some order of operationsconsiderations thrown in. As long as you're careful with the minus signs, and don't confuseaddition and multiplication, you should do fine.

There are a couple formats for adding and subtracting, and they hearken back to earlier times, when you were adding and subtracting just plain old numbers. First, you learned addition "horizontally", like this:6 + 3 = 9. You can add polynomials in the same way, grouping like terms and then simplifying.

• Simplify (2x + 5y) + (3x – 2y)

I'll clear the parentheses, group like terms, and then simplify:

(2x + 5y) + (3x – 2y) 
  =  2x + 5y + 3x – 2y 
  =  2x + 3x + 5y – 2y 
  =  5x + 3y

          Horizontal addition works fine for simple examples. But when you were adding plain old numbers, you didn't generally try to add 432 and 246 horizontally; instead, you would "stack" them vertically, one on top of the other, and then add down the columns:

432 + 246 = 672

You can do the same thing with polynomials. This is how the above simplification exercise looks when it is done "vertically":

From: http://www.purplemath.com/modules/polyadd.htm

Quiz in math lp from Lorna1125

Algebraic Expressions

Variables and Algebraic Expressions

        A variable is a symbol used to denote any element of a given set—often a letter used to stand for number. Variables are used to change verbal expressions into algebraic expressions.

Give the algebraic expression.

Verbal Expression	Algebraic Expression
The sum of a number n and 7	n + 7 or 7 + n
The number n diminished by 10	n – 10
Seven times the number n	7 n
x divided by 4
Five more than the product of 2 and n	2 n + 5 or 5 + 2 n
Seven less than the quotient of y and 4

From: http://www.cliffsnotes.com/math/algebra/algebra-i/terminology-sets-and-expressions/variables-and-algebraic-expressions

Algebraic Expressions

Writing Algebraic Expressions

 

Problem:   Ms. Jensen likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.  [IMAGE]
Solution:   Let g represent the number of groups in Ms. Jensen's class.
  Then 2 · g, or 2g can represent "g groups of 2 students".

In the problem above, the variable g represents the number of groups in Ms. Jensen's class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number can vary (change). Let's look at an example in which we use a variable.

Example 1:     Write each phrase as a mathematical expression.

 
Phrase Expression
the sum of nine and eight 9 + 8
the sum of nine and a number x 9 + x

The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.

From: http://www.mathgoodies.com/lessons/vol7/expressions.html