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2014-07-12T17:22:45+08:00

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A³ ± b³  =  (a ± b) (a² ∓ ab + b²)


1)   a=8x  ;   b=y
   512x³ - y³ = (8x - y) (64x² + 8xy + y²)


2)  a=4m   ;   b=9
    64m³ + 729 = (4m + 9) (16m² - 36m + 81)


3)  a=10n   ;   b=5m
     1000n³ - 125m³  =  (10n - 5m) (100n² + 50mn + 25m²)

We may still factor out 5 from (10n - 5m) and 25 from (100n² + 50mn + 25m²), so

5 (2n - m) · 25 (4n² + 4mn + m²)  =  125 (2n - m) (4n² + 4mn + m²)
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I just noticed that I made a mistake in #3. The last factor should be (4n² + 2mn + m²) and not (4n² + 4mn + m²)