?1/Phân tích đa thức -> nhân tử
bc(b+c)+ca(c-a)-ab(a+b)
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M=(a-b)(a2+ab+b2)-3ab
= a2+ab+b2-3ab
=a2-2ab+b2
=(a-b)2=12=1
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a+b=c+d
(a+b)2=(c+d)2
a2+2ab+b2=c2+2cd+d2
ma a2+b2=c2+d2
2ab=2cd nen -2ab=-2cd
a2+b2=c2+d2
a2-2ab+b2=c2-2cd+d2
(a-b)2=(c-d)2
a-b=c-d hoac a-b=d-c
ma a+b=c+d
nen a=c hoac a=d
nen a=c;b=d hoac a=d;b=c
nen a2013=c2013;b2013=d2013 hoac a2013=d2013;b2013=c2013
Vay a2013+b2013=c2013+d2013 trong ca 2 truong hop
QUA DE
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bạn có: x^4 + 2016x^2 + 2015x + 2016
= x^4 + x^3 + x^2 - x^3 - x^2 - x + 2016x^2 + 2016x + 2016
= x^2(x^2 + x + 1) - x(x^2 + x + 1) + 2016(x^2 + x + 1)
= (x^2 + x + 1)(x^2 - x + 2016)
\(x^4+2016x^2+2015x+2016\)
=\(x^4+x^3+x^2+2015x^2+2015x+2015+1-x^3\)
=\(x^2\left(x^2+x+1\right)+2015\left(x^2+x+1\right)+\left(1-x\right)\left(x^2+x+1\right)\)
=\(\left(x^2+x+1\right)\left(x^2+2015+1-x\right)\)
=\(\left(x^2+x+1\right)\left(x^2-x+2016\right)\)
bc(b+c)+ca(c-a)-ab(a+b)
=bc(b+c)+ca(b+c)-ca(a+b)-ab(a+b)
=c(a+b)(b+c)-a(a+b)(b+c)
=(c-a)(a+b)(b+c)