Calculate. x 6 − 54

Question

Calculate.       x          6        −  54

Ismailatirf · Accepted Answer

First you know that       x    6   can be factored into  (      x    3    )  (      x    3    )You also know that 64 can be factored into (8)(8).So when you have a problem in a form such as that, eg....      x    2    −      a    2   ....you can factor into (x-a)(x+a)So you get:   (      x    3    +  8  )  (      x    3    −  8  )

Moselq8 · Accepted Answer

(      x    3    +  8  )  (      x    3    −  8  )...Sum of Cubes      a          3        –      b          3        =  (  a  –  b  )  (      a          2        +  a  b  +      b          2        )...Difference of Cubes  (      x    3    +  8  )  =  (      x    3    +      2    3    )  =  (  x  +  2  )  (      x    2    −  2  x  +  4  )  (      x    3    −  8  )  =  (      x    3    −      2    3    )  =  (  x  −  2  )  (      x    2    +  2  x  +  4  )Final answer:      x          2        −  64  =  (  x  +  2  )  (      x          2        −  2  x  +  4  )  (  x  −  2  )  (      x          2        +  2  x  +  4  )

Calculate. x^6 -64

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