Question 1178730
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<pre>
Formally,  81-x^2  can be presented / factored as


    81-x^2 = -(x+9)*(x-9).



Formally,  -(x+9)*(x-9)  is IDENTICALLY the same as  (9+x)*(9-x).


So, formally your son's answer is correct.


But  (9+x)*(9-x)  is  <U>traditionally</U>  considered as  "more simple"  comparing with  -(x+9)*(x-9).
</pre>


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On these simple factoring formulas, see the lessons



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.