Question 1093004
.
<pre>
{{{x - 64x^3}}} = {{{x*(1-64x^2)}}} =   (  apply the formula {{{a^2 - b^2}}} = (a+b)*(a-b) to get )

= {{{x*(1+8x)*(1-8x)}}}.
</pre>

<U>Answer</U>.  {{{x - 64x^3}}} = {{{x*(1+8x)*(1-8x)}}}.


Solved.



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The shortcut quadratic multiplication formulas:



1. The <B>square of the sum formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{(a + b)^2 = a^2 + 2ab +b^2}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The_square_of_a_sum.lesson>The square of the sum formula</A> in this site.



2. The <B>square of the difference formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;{{{(a - b)^2 = a^2 - 2ab +b^2}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The_square_of_a_difference.lesson>The square of the difference formula</A> in this site.



3. The <B>difference of squares formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{a^2 - b^2 = (a + b)*(a- b)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The_difference_of_squares_formula.lesson>The difference of squares formula</A>  in this site.




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