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Papessa [141]
3 years ago
9

How would you factor a^3 - b^3? Please leave detailed instructions. Thanks so much!

Mathematics
1 answer:
Sindrei [870]3 years ago
4 0

<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)

You can see why this works if you expand the right side as

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

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

Both the <em>a</em>²<em>b</em> and <em>ab</em>² terms cancel, leaving you with <em>a</em>³ - <em>b</em>³.

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Step-by-step explanation:

Given that :

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