# GED Math : Single-Variable Algebra

## Example Questions

### Example Question #21 : Simplifying, Distributing, And Factoring

Simplify completely:

Explanation:

### Example Question #21 : Simplifying, Distributing, And Factoring

Subtract   from .

Explanation:

Explanation:

### Example Question #24 : Algebra

Factor completely:

Explanation:

First, factor out the greatest common factor of the terms, which is :

The quadratic trinomial can be factored as  where  and ; by trial and error we find that the numbers chosen are , so

### Example Question #25 : Algebra

Simplify:

Explanation:

Apply the power of a quotient rule:

### Example Question #23 : Algebra

Factor completely:

Explanation:

is a common factor of both terms, so factor it out:

cannot be factored, so this is the complete factorization.

### Example Question #27 : Algebra

Factor completely:

Explanation:

First, we find two integers whose sum is 19 and whose product is . Through trial and error we find these integers are 3 and 16. We use these numbers to split the middle term, then we factor using the grouping method:

### Example Question #581 : Ged Math

Factor completely:

Explanation:

Factor by grouping as follows:

### Example Question #581 : Ged Math

Factor completely:

Explanation:

Factor by grouping as follows:

The first factor is the difference of squares, so further factoring can be done:

### Example Question #30 : Algebra

Factor completely: