Toán Lớp 8: x^3-y^3+xy(x-y)=(x-y)(x+y)^2
Lm nhanh hộ mik vs ạ
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: x^3-y^3+xy(x-y)=(x-y)(x+y)^2
Lm nhanh hộ mik vs ạ
Comments ( 2 )
Giải đáp+Lời giải và giải thích chi tiết:
x3 + y3 – xy( x + y ) = ( x + y )( x – y )2
x3 + y3 – xy( x + y )
= x3 + y3 – x2y – xy2
= x3 + 3x2y + 3xy2 + y3 – 4x2y – 4xy2
= ( x3 + 3x2y + 3xy2 + y3 ) – 4xy( x + y )
= ( x + y )3 – 4xy( x + y )
= ( x + y )[ ( x + y )2 – 4xy ]
= ( x + y )( x2 + 2xy + y2 – 4xy )
= ( x + y )( x2 – 2xy + y2 )
= ( x + y )( x – y )2
Mong đc câu trả lời hay nhất ạ
$x^3-y^3+xy\left(x-y\right)=\left(x-y\right)\left(x+y\right)^2$
Ta có: VT= $x^3-y^3+xy\left(x-y\right)$
$=x^3-y^3+xyx-xyy$
$=x^3-y^3+x^2y-xy^2$
$=x^3+x^2y-xy^2-y^3$
$=\left(x^3+x^2y\right)+\left(-xy^2-y^3\right)$
$=x^2\left(x+y\right)-y^2\left(x+y\right)$
$=\left(x+y\right)\left(x^2-y^2\right)$
$=\left(x+y\right)\left(x+y\right)\left(x-y\right)$
$=\left(x+y\right)^2\left(x-y\right)$ =VP (ĐPCM)