toán lớp 8

T

thaolovely1412


b) ta có:[TEX]x - y + y - z + z - x = 0 [/TEX]
áp dụng: nếu a+b+c=0 thì [TEX]a^3+b^3+c^3=3abc[/TEX] ta được:
[TEX](x-y)^3 + (y - z)^3 + (z - x)^3 = 3(x-y) (y-z) (z-x)[/TEX]
 
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T

thaolovely1412

c)[TEX]x^4+2014x^2+2013x+2014[/TEX]
[TEX]= x^4-x+2014x^2+2014x+2014[/TEX]
[TEX]= x(x^3-1)+2014(x^2+x+1)[/TEX]
[TEX]= x(x-1)(x^2+x+1)+2014(x^2+x+1)[/TEX]
[TEX]= (x^2+x+1)(x^2-x+2014)[/TEX]
 
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C

chonhoi110

a) $a^3(b^2 - c^2) + b^3( c^2 - a^2) + c^3(a^2 - b^2)$
$=a^3(b^2 - c^2) - b^3(b^2- c^2 + a^2-b^2) + c^3(a^2 - b^2)$
$=a^3(b^2 - c^2) - b^3(b^2- c^2) - b^3(a^2-b^2) + c^3(a^2 - b^2)$
$=(b^2-c^2)(a^3-b^3)-(a^2-b^2)(b^3-c^3)$
$=(b-c)(b+c)(a-b)(a^2+ab+b^2)-(a-b)(a+b)(b-c)(b^2+bc+c^2)$
$=(a-b)(b-c)[(b+c)(a^2+ab+b^2)-(a+b)(b^2+bc+c^2)]$
$=(a-b)(b-c)(a^2c-bc^2-ac^2+a^2b)$
$=(a-b)(b-c)(a-c)(ab+ac+bc)$
 
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