Notes: Pls. help me factor these given, i'm new to factoring, a raised to 9 minus b raised to 9 a^9

Tuesday, March 31, 2015

Pls. help me factor these given, i'm new to factoring, a raised to 9 minus b raised to 9 a^9 - b^9the ^ sign is exponent, thx

This is the difference of two cubes and it returns the
product:

$\displaystyle{{a}}^{{{9}}}$ - $\displaystyle{{b}}^{{{9}}}$ = $\displaystyle{{a}}^{{{3}\cdot{3}}}$ - $\displaystyle{{b}}^{{{3}\cdot{3}}}$ =
( $\displaystyle{{a}}^{{{3}}}$ - $\displaystyle{{b}}^{{{3}}}$ )( $\displaystyle{{a}}^{{{3}\cdot{2}}}$ + $\displaystyle{{a}}^{{{3}}}$ * $\displaystyle{{b}}^{{{3}}}$ + $\displaystyle{{b}}^{{{3}\cdot{2}}}$
)

$\displaystyle{{a}}^{{{9}}}$ - $\displaystyle{{b}}^{{{9}}}$ = ( $\displaystyle{{a}}^{{{3}}}$ - $\displaystyle{{b}}^{{{3}}}$ )( $\displaystyle{{a}}^{{{6}}}$ +
$\displaystyle{{a}}^{{{3}}}$ * $\displaystyle{{b}}^{{{3}}}$ + $\displaystyle{{b}}^{{{6}}}$ )

We notice that the 1st factor
is also a difference of two cubes:

$\displaystyle{{a}}^{{{9}}}$ - $\displaystyle{{b}}^{{{9}}}$ = (a -
b)( $\displaystyle{{a}}^{{{2}}}$ + ab + $\displaystyle{{b}}^{{{2}}}$ )( $\displaystyle{{a}}^{{{6}}}$ + $\displaystyle{{a}}^{{{3}}}$ * $\displaystyle{{b}}^{{{3}}}$ + $\displaystyle{{b}}^{{{6}}}$
)

The factorized expression is $\displaystyle{{a}}^{{{9}}}$ -
$\displaystyle{{b}}^{{{9}}}$ = (a-b)( $\displaystyle{{a}}^{{{2}}}$ + ab + $\displaystyle{{b}}^{{{2}}}$ )( $\displaystyle{{a}}^{{{6}}}$ + $\displaystyle{{a}}^{{{3}}}$ * $\displaystyle{{b}}^{{{3}}}$ + $\displaystyle{{b}}^{{{6}}}$
).

Notes

Tuesday, March 31, 2015

Pls. help me factor these given, i'm new to factoring, a raised to 9 minus b raised to 9 a^9 - b^9the ^ sign is exponent, thx

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What is the meaning of the 4th stanza of Eliot's Preludes, especially the lines "I am moved by fancies...Infinitely suffering thing".

Tuesday, March 31, 2015

Pls. help me factor these given, i'm new to factoring, a raised to 9 minus b raised to 9 a^9 - b^9the ^ sign is exponent, thx

No comments:

Post a Comment

What is the meaning of the 4th stanza of Eliot&#39;s Preludes, especially the lines &quot;I am moved by fancies...Infinitely suffering thing&quot;.

What is the meaning of the 4th stanza of Eliot's Preludes, especially the lines "I am moved by fancies...Infinitely suffering thing".