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Deffense [45]
3 years ago
12

Explain how to use a polynomial identity to factor x^6-27y^3

Mathematics
2 answers:
Umnica [9.8K]3 years ago
6 0
Dont really no sorry
Taya2010 [7]3 years ago
5 0

This is a sum of cubes:

<em>x</em>⁶ - 27<em>y</em>³ = (<em>x</em>²)³ + (-3<em>y</em>)³

Recall that

<em>a</em>³ + <em>b</em>³ = (<em>a</em> + <em>b</em>) (<em>a</em>² - <em>ab</em> + <em>b</em>²)

So we have

<em>x</em>⁶ - 27<em>y</em>³ = (<em>x</em>² - 3<em>y</em>) ((<em>x</em>²)² - <em>x</em>² (-3<em>y</em>) + (-3<em>y</em>)²)

<em>x</em>⁶ - 27<em>y</em>³ = (<em>x</em>² - 3<em>y</em>) (<em>x</em>⁴ + 3<em>x</em>²<em>y</em> + 9<em>y</em>²)

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