Easy Algebra Step-by-Step

90 Easy Algebra Step-by-Step

of real numbers to rearrange the expression so that matching like terms are

together (later, you might choose do this step mentally). If the expression

includes unlike terms, just indicate the sums or differences of such terms.

To avoid sign errors as you work, keep a − symbol with the number that fol-

lows it.

Problem Simplify xx^3255555 x^2 − 10 xx++ 2525255 2273277 xx − 5.

Solution

Step 1. Check for like terms.

4 xx^3255555 x^2 − 10 xx++ 25252525 2273277 xx − 5

The like terms are 42 xx^3322 , 57 xx^2277 , and 25 and 5.

Step 2. Rearrange the expression so that like terms are together.

4 xx^3255555 x^2 − 10 xx++ 25252525 2273277 xx − 5

= 42 x^3 + xxx^322 +++ 5757 − 7717 − 02 x+ 55 −

Step 3. Systematically combine matching like

terms and indicate addition or subtraction

of unlike terms.

= 6 xx^3222222 x^2 − 10 x+ 20

= 6x^32 −−2x2x 2 10 x+ 20

Step 4. Review the main result.

4 xx^3255555 x^2 − 10 xx++ 25252525 2273277 xxx 56566 x^32 − 221 xx 11100200 0

Addition and Subtraction of Polynomials

Addition of Polynomials

To add two or more polynomials, add like monomial terms and simply

indicate addition or subtraction of unlike terms.

Problem Perform the indicated addition.

a. ()^22 ))) ((()(((

b. ()^32 ))))) (((()^3

When you are simplifying,

rearrange so that like terms are

together can be done mentally.

However, writing out this step

helps you avoid careless errors.

Because + – is equivalent to –,

it is customary to change + – to

simply – when you are simplifying

expressions.

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