Toán Lớp 8: Phân tích đa thức thành nhân tử: (x^2 + y^2)^3 + (z^2 – x^2)^3 – (y^2 + z^2)^3
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 8: Phân tích đa thức thành nhân tử: (x^2 + y^2)^3 + (z^2 – x^2)^3 – (y^2 + z^2)^3
Comments ( 2 )
=(x^2)^3+3.(x^2)^2 .y²+3.x².(y^2)^2+(y^2)^3+(z^2)^3-3.(z^2)^2 .x²+3.z².(x^2)^2-(x^2)^3-[(y^2)^3+3.(y^2)^2 .z²+3.y².(z^2)^2+(z^2)^3]
=x^6+3x^4y²+3x²y^4+y^6+z^6-3x²z^4+3x^4z²-x^6-(y^6+3y^4z^2+3y^2z^4+z^6)
=x^6+3x^4y²+3x²y^4+y^6+z^6-3x²z^4+3x^4z²-x^6-y^6-3y^4z^2-3y^2z^4-z^6
=(x^6-x^6)+(y^6-y^6)+(z^6-z^6)+3x^4y^2+3x^2y^4-3x^2z^4+3x^4z^2-3y^4z^2-3y^2z^4
=3x^4y^2+3x^2y^4-3x^2z^4+3x^4z^2-3y^4z^2-3y^2z^4
=3x^4y^2+3x^2y^4-3x^2z^4+3x^4z^2-3y^4z^2-3y^2z^4+3x^2y^2z^2-3x^2y^2z^2
=3(x^4y^2+x^2y^4-x^2z^4+x^4z^2-y^4z^2-y^2z^4-x^2y^2z^2+x^2y^2z^2)
=3[-(x^2z^4+y^2z^4-x^2y^2z^2-x^4z^2)-(y^4z^2-x^2y^4+x^2y^2z^2-x^4y^2)]
=3[-z^2(x^2z^2+y^2z^2-x^2y^2-x^4)-y^2(y^2z^2-x^2y^2+x^2z^2-x^4)]
=3[-z^2(x^2z^2+y^2z^2-x^2y^2-x^4)-y^2(x^2z^2+y^2z^2-x^2y^2-x^4)]
=3(-z^2-y^2)(x^2z^2+y^2z^2-x^2y^2-x^4)
=-3(y^2+z^2)(x^2z^2+y^2z^2-x^2y^2-x^4)
=-3(y^2+z^2)[z^2(x^2+y^2)-x^2(x^2+y^2)]
=-3(y^2+z^2)(x^2+y^2)(z^2-x^2)
=3(y^2+z^2)(x^2+y^2)(x^2-z^2)
=3(y^2+z^2)(x^2+y^2)(x+z)(x-z)