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About LinkBacksDoes anyone know how to derive the factor formulas for sum and difference of cubes? that is
 (a^2 + ab + b^2)<br />
)
Originally Posted by skylabel
Does anyone know how to derive the factor formulas for sum and difference of cubes? that is
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I have just multiplied the factors to show you the steps
Another method is to do the polynomial long division:
[HTML] a^2 + ab + b^2
--------------------------
a - b )a^3 + 0a^2b + 0ab^2 - b^3
a^3 - 1a^2b
--------------------------
1a^2b + 0ab^2 - b^3
1a^2b - 1ab^2
--------------------------
1ab^2 - b^3
1ab^2 - b^3
--------------------------
0[/HTML]
To elaborate:Another method is to do the polynomial long division:
[html] a^2 + ab + b^2
--------------------------
a - b )a^3 + 0a^2b + 0ab^2 - b^3
a^3 - 1a^2b
--------------------------
1a^2b + 0ab^2 - b^3
1a^2b - 1ab^2
--------------------------
1ab^2 - b^3
1ab^2 - b^3
--------------------------
0[/html]
Since a^3 - b^3 is equal to zero when a = b, it's obvious that a - b is a factor of a^3 - b^3.
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