phân tích `10x(x-y)-6y(y-x)` `3x^2 + 5y-3xy-5x` `3y^2-3z^2+3x^2+6xy` `16x^3+54y^3` `x^2-25-2xy+y^2` `x^5-3x^4+3x^3-x^2`

2 bình luận về “phân tích `10x(x-y)-6y(y-x)` `3x^2 + 5y-3xy-5x` `3y^2-3z^2+3x^2+6xy` `16x^3+54y^3` `x^2-25-2xy+y^2` `x^5-3x^4+3x^3-x^2`”

1. Giải đáp + Lời giải và giải thích chi tiết:

    10x(x-y)-6y(y-x)

   = 10x(x-y) + 6y(x-y)

   = (x-y)(10x+6y)

   = 2(x-y)(5x+3y)

   _______

   3x^2 + 5y – 3xy-5x

   = (3x^2 -3xy)+(5y-5x)

   = 3x(x-y)-5(x-y)

   = (x-y)(3x-5)

   ________

   3y^2-3z^2+3x^2+6xy

   = 3(y^2 – z^2 + x^2 + 2xy)

   = 3[(x^2+2xy+y^2)-z^2]

   = 3[(x+y)^2-z^2]

   = 3(x+y-z)(x+y+z)

   _________

   16x^3 + 54 y^3

   = 2(8x^3 + 27y^3)

   = 2[(2x)^3 + (3y)^3]

   = 2(2x+3y)[(2x)^2 – 2x.3y + (3y)^2]

   = 2(2x+3y)(4x^2-6xy+ 9y^2)

   __________

   x^2-25-2xy+y^2

   = (x^2 – 2xy+y^2)-25

   = (x-y)^2-5^2

   = (x-y-5)(x-y+5)

   _________

   x^5-3x^4+3x^3-x^2

   = x^2(x^3 – 3x^2+3x-1)

   = x^2(x^3 – 3.x^2 .1+3.x.1^2+1^3)

   = x^2(x-1)^3

   Trả lời
2. Giải đáp:

    10x.(x-y)-6y.(y-x)

   =10x.(x-y)+6y.(x-y)

   =(x-y).(10x+6y)

   =2.(x-y).(5x+3y)

   ______________

   3x^{2}+5y-3xy-5x

   =(3x^{2}-3xy)-(5x-5y)

   =3x.(x-y)-5.(x-y)

   =(x-y).(3x-5)

   ______________

   3y^{2}-3z^{2}+3x^{2}+6xy

   =3.(y^{2}-z^{2}+x^{2}+2xy)

   =3.[(x^{2}+2xy+y^{2})-z^{2}]

   =3.[(x+y)^{2}-z^{2}]

   =3.(x+y-z).(x+y+z)

   __________________

   16x^{3}+54y^{3}

   =16.x^{3}+16.\frac{27}{8}y^{3}

   =16.(x^{3}+\frac{27}{8}y^{3})

   =16.[x^{3}+(\frac{3}{2}y)^{3}]

   =16.(x+\frac{3}{2}y).[x^{2}-x.\frac{3}{2}y+(\frac{3}{2}y)^{2}]

   =16.(x+\frac{3}{2}y).(x^{2}-\frac{3}{2}xy+\frac{4}{9}y^{2})

   ________________

   x^{2}-25-2xy+y^{2}

   =(x^{2}-2xy+y^{2})-25

   =(x^{2}-2.x.y+y^{2})-25

   =(x-y)^{2}-5^{2}

   =(x-y-5).(x-y+5)

   ________________

   x^{5}-3x^{4}+3x^{3}-x^{2}

   =(x^{5}-x^{2})-(3x^{4}-3x^{3})

   =x^{2}.(x^{3}-1)-3x^{3}.(x-1)

   =x^{2}.(x-1).(x^{2}+x+1)-3x^{3}.(x-1)

   =(x-1).[x^{2}.(x^{2}+x+1)-3x^{3}]

   =(x-1).(x^{4}+x^{3}+x^{2}-3x^{3})

   =(x-1).(x^{4}-2x^{3}+x^{2})

   =x^{2}.(x-1).(x^{2}-2x+1)

   =x^{2}.(x-1).(x-1)^{2}

   =x^{2}.(x-1)^{3}

   Trả lời