представьте многочлен в виде произвидения: ...

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представьте многочлен в виде произвидения: 1.ах²-bx²-bx+ax-a+b 2.ax²+bx²-bx-ax+a+b 3.ax²+bx²+ax-cx²+bx-cx 4.ax²+bx²-bx-ax+cx²-cx

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VekaSolnce

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$ax^{2}-bx^{2}-bx+ax-a+b=x^{2}(a-b)+x(a-b)-(a-b)=$

$(x^{2}+x-1)(a-b)$

$ax^{2}+bx^{2}-bx-ax+a+b=x^{2}(a+b)-x(a+b)+(a+b)=$

$=(x^{2}-x+1)(a+b)$

$ax^{2}+bx^{2}+ax-cx^{2}+bx-cx=x^{2}(a+b-c)+x(a+b-c)=$

$=(a+b-c)(x^{2}+x)=x (a+b-c)(x+1)$

$ax^{2}+bx^{2}-bx-ax+cx^{2}-cx=x^{2}(a+b+c)-x(a+b+c)=$

= $(x^{2}-x)(a+b+c)=x(a+b+c)(x-1)$

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