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Factoring the Sum and Difference of Cubes

Forumulas

Sum of Cubes :

Difference of Cubes :

Expand these formulas to show that they are correct.

Example 1 Factor: y^3 - 8

 

Example 2 Factor: z^3 + 125

 

Recalling the Difference of Squares Formula
Difference of Squares:

Example 3 Factor: 25x^2 - 81

 

General Rules for Factoring

1. Factor out the GCF .
2. Identify whether the polynomial has two terms , three terms, or more
than three terms.
3. If the polynomial has more than three terms, try factoring by grouping.
4. If the polynomial has three terms, check first for a perfect square trinomial.
Otherwise, factor the trinomial with the grouping method (or the trial and error method).
5. If the polynomial has two terms , determine if it fits the pattern for
  (a) a Difference of squares, or
  (b) a Difference of cubes , or
  (c) A sum of cubes .
6. Be sure to factor completely.
7. Check your answer by multiplying .
 

Example 4 Factor: 3ac + ad - 3bc - bd

 

Example 5 Factor: -2x^2 + 8x - 8

 

Example 6 Factor: -p^3 - 5p^2 - 4p

 

Steps for Factoring Trinomials by Grouping

Your trinomial has the form ax^2 + bx + c.
1. Identify a, b, and c.
2. Find m and n such that mn = ac and m + n = b.
3. Rewrite your original trinomial as ax^2 + mx + nx + c.
4. Group the first two terms and the last two terms and factor each of them.
5. Finish by factoring the common binomial from the two resulting terms.

Example 7 Factor: 7p^2 - 29p + 4
1. Identify a, b, and c.
2. Find m and n such that mn = ac and m + n = b.

3. Rewrite your original trinomial as ax^2 + mx + nx + c.

4. Group the first two terms and the last two terms and factor each of
them.

5. Finish by factoring the common binomial from the two resulting terms.

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