Hi, I'm reading a book (Israel M. Gelfand, Alexander Shen Algebra 1993) and I have some troubles with some exercises, can you help me to understand this please?
Here are the exercises
122. Factor b. x (y^2 - Z^2 ) + y(z^2 - X^2 ) + z(x^2 - y^2 ); c. a^10 + a^5 + 1; d. a^3 + b^3 + c^3 - 3abc ; e. (a+b+c)^3 - a^3-b^3-c^3; f. (a - b)^3 + (b - c)^3 + (c - a)^3
3 comments:
Hi, I'm reading a book (Israel M. Gelfand, Alexander Shen Algebra 1993) and I have some troubles with some exercises, can you help me to understand this please?
Here are the exercises
122. Factor
b. x (y^2 - Z^2 ) + y(z^2 - X^2 ) + z(x^2 - y^2 );
c. a^10 + a^5 + 1;
d. a^3 + b^3 + c^3 - 3abc ;
e. (a+b+c)^3 - a^3-b^3-c^3;
f. (a - b)^3 + (b - c)^3 + (c - a)^3
Thank you so much.
too many question)
here I go with hints
b)
x(y^2-z^2) + y(z^2-x^2) + z(x^2-y^2)
= x(y^2-z^2) + x^2(y-z) + yz(y-z)
take y- z common and proceed.
c)
refer to http://in.answers.yahoo.com/question/index;_ylt=ApMTtSXfn_PdlGGk.3eY3k.RHQx.;_ylv=3?qid=20070419040840AA9Za18
f)
if x + y + z = 0 then x^3 + y^3 + z^3 = 3xyz
as (a-b) + (b-c)+ (c-a) = 0 we get
(a-b)^3 + (b-c)^3+ (c-a)^3 = 3 (a-b)(b-c)(c-a)
e) refer to mu blog entry Jan 28/2011 under algebra section
d) can be found in some standard book of maths.
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