Question

Using complete sentences, explain how you would factor completely x^9 – 64.

Answer 1

8^2=64

Answer 2

4^3=64

Answer 3

Think of it like difference of cubes.\[(x^3)^3 - 4^3 \]

Answer 4

\[a^3 - b^3 \implies (a - b)(a^2 + ab + b^2) \]

Answer 5

... and then simplify.

Answer 6

the a,b,c, is confusing me can you show me using the numbers in the problem?

Answer 7

a=x and b=4

Answer 8

im still really confused how would i factor x^9-64 like how would i split up the terms

Answer 9

@ghazi \(a = x^3\)

Answer 10

@ParthKohli :(

Answer 11

@lukelebeau You could also go with this.\[ \large {a^9 - b^9} \implies (a - b) (a^2 + a b + b^2) (a^6 + a^3 b^3 + b^6)\]

Answer 12

@lukelebeau see \[(x^3)^3-4^3=(x^3-4)((x^3)^2+4*x^3+4^2)\]

Answer 13

so we facor x^9 first which is (x^3)^3?

Answer 14

yes