Factor completely. h^6-64

Name: Problem 97, Chapter 7: Beginning and Intermediate Algebra
Uploaded: 2020-07-01T23:11:59-08:00
Duration: 1 min 15 s
Channel: Cory Kuzinski
Description: Factor completely. h^6-64

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Key Concepts

Difference of Squares

The technique of factoring a difference of squares is used when an expression can be written in the form a² - b². It factors into (a - b)(a + b), which simplifies the expression by breaking it into two binomial factors. This method is fundamental in algebra for simplifying and solving polynomial equations.

Sum and Difference of Cubes

Expressions in the form a³ + b³ and a³ - b³ can be factored using the sum and difference of cubes formulas. Specifically, a³ - b³ factors into (a - b)(a² + ab + b²) and a³ + b³ factors into (a + b)(a² - ab + b²). This concept is crucial for further reducing polynomials that include cubic terms.

Recursive or Nested Factoring

Recursive or nested factoring involves applying multiple factoring techniques sequentially. After the initial factorization has been performed, the resulting factors are examined to see if they can be factored further, allowing the expression to be completely broken down into irreducible factors. This systematic approach is essential for fully simplifying complex algebraic expressions.

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