$\displaystyle y^2 - 343 = x^{3} - 3(x^{2})(7) + 3(x)(49)-343$

to

$\displaystyle y^2 - 7^3 = (x-7)^3$

Is there a specific name for the second one? Could you please explain how to get from the first to the second.

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- Apr 13th 2010, 08:24 AMericforman65How was this simplified?
$\displaystyle y^2 - 343 = x^{3} - 3(x^{2})(7) + 3(x)(49)-343$

to

$\displaystyle y^2 - 7^3 = (x-7)^3$

Is there a specific name for the second one? Could you please explain how to get from the first to the second. - Apr 13th 2010, 09:53 AMmasters
Hi ericforman65,

$\displaystyle y^2-343=y^2-7^3$ on the left.

The right side was obtained from $\displaystyle x^3-3x^3(7)+3x^2(49)+349$ by recognizing the binomial expansion of $\displaystyle (x-7)^3$

Remember the binomial theorem?

$\displaystyle (x-a)^3=x^3a^0-3x^2a^1+3x^1a^2-a^3$

Now, let a = 7

$\displaystyle (x-7)^3=x^3(7^0)-3x^2(7^1)+3x(7^2)-7^3$

$\displaystyle (x-7)^3=x^3-3x^2(7)+3x(49)-343$