РАЗЛОЖИТЕ НА МНОЖИТЕЛИ(895-897)
895
Б)a+b-a^2+b^2
Г)m-m^2-n+n^2
896
б)b^2-bc-a^2+ac
г)x^2y^2+1-y^2-x^2
897
б)xy^2+x^2y-x^3-y^3
г)a^3-3a^2b+3ab^2-b^3
б) a+b-a^2+b^2=
= (a+b)-(a^2-b^2)=
=(a+b)-(a-b)(a+b)=
=(a+b)(1-a+b)
г) m-m^2-n+n^2=
=(m-n)-(m^2-n^2)=
=(m-n)(1-m-n)
б) b^2-bc-a^2+ac=
=-a^2+ab-ab+b^2+ac-bc=
=-(a^2-ab)-(ab-b^2)+(ac-bc)=
=-a(a-b)-b(a-b)+c(a-b)=
=(a-b)(c-a-b)
г) - не понятная запись
б) xy^2+x^2y-x^3-y^3=
=(xy^2-y^3)-(x^3-x^2y)=
=y^2(x-y)-x^2(x-y)=
=(y^2-x^2)(x-y)=
=(y-x)(y+x)(x-y)
г) a^3-3a^2b+3ab^2-b^3=
=(a^3-b^3)-(3a^2b-3ab^2)=
=(a-b)(a^2+ab+b^2)-(a-b)3ab=
=(a^2+ab+b^2-3ab)(a-b)=
=(a^2-2ab+b^2)(a-b)=
=(a-b)^2(a-b)=
=(a-b)^3
б) (b-a+1)(b+a)
г) (n-m)(n+m-1)
б) (a-b)(c-b-a)
г) (x-1)(x+y)(y-1)(y+1)
б) (-y^2+2xy-x^2)(y+x)
г) -(b-a)^3
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Answers & Comments
б) a+b-a^2+b^2=
= (a+b)-(a^2-b^2)=
=(a+b)-(a-b)(a+b)=
=(a+b)(1-a+b)
г) m-m^2-n+n^2=
=(m-n)-(m^2-n^2)=
=(m-n)(1-m-n)
б) b^2-bc-a^2+ac=
=-a^2+ab-ab+b^2+ac-bc=
=-(a^2-ab)-(ab-b^2)+(ac-bc)=
=-a(a-b)-b(a-b)+c(a-b)=
=(a-b)(c-a-b)
г) - не понятная запись
б) xy^2+x^2y-x^3-y^3=
=(xy^2-y^3)-(x^3-x^2y)=
=y^2(x-y)-x^2(x-y)=
=(y^2-x^2)(x-y)=
=(y-x)(y+x)(x-y)
г) a^3-3a^2b+3ab^2-b^3=
=(a^3-b^3)-(3a^2b-3ab^2)=
=(a-b)(a^2+ab+b^2)-(a-b)3ab=
=(a^2+ab+b^2-3ab)(a-b)=
=(a^2-2ab+b^2)(a-b)=
=(a-b)^2(a-b)=
=(a-b)^3
Verified answer
895
б) (b-a+1)(b+a)
г) (n-m)(n+m-1)
896
б) (a-b)(c-b-a)
г) (x-1)(x+y)(y-1)(y+1)
897
б) (-y^2+2xy-x^2)(y+x)
г) -(b-a)^3