\(2x^3y-2xy^3-4xy^2-2xy\)

\(=2xy.\left(x^2-y^2-2y-1\right)\)

\(=2xy.[x^2-\left(y^2+2y+1\right)]\)

\(=2xy.[x^2-\left(y+1\right)^2]\)

\(=2xy.\left(x+y+1\right).\left(x-y-1\right)\)

Vậy chọn đáp án A

chọn A

nhìn đề bài rắc rối thế

A=x2−2xy−4x+2y2−8y+20C=x2−2xy−4x+2y2−8y+20

=(x2−2xy+y2)−4(x−y)+4+y2−12y+36−20=(x2−2xy+y2)−4(x−y)+4+y2−12y+36−20

=(x−y)2−4(x−y)+4+(y−6)2−20=(x−y)2−4(x−y)+4+(y−6)2−20

=(x−y−2)2+(y−6)2−20≥−20∀x;y=(x−y−2)2+(y−6)2−20≥−20∀x;y

Dấu " = " xảy ra ⇔{x−y−2=0y−6=0⇔{x−y=2y=6⇔{x−y−2=0y−6=0⇔{x−y=2y=6

⇔x=8;y=6⇔x=8;y=6

Vậy  A là : −20⇔x=8;y=6

(4x²+2xy+y²)(2x-y)-(2x-y)(4x²-2xy+y²)

=(2x³-y³)-(2x+y)(4x²-2xy+y²)

=(2x³-y³)-(2x³+y³)

=2x³-y³-2x³+y³

=0

( 2x + y ) ( 4x² - 2xy + y² ) - ( 2x - y ) ( 4x² + 2xy + y² )

= 8x³ + y³ - ( 8x³ - y³ )
= 2y³ 

\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

\(=8x^3+y^3-\left(8x^3-y^3\right)\)

\(=8x^3+y^3-8x^3+y^3\)

\(=\left(8x^3-8x^3\right)+\left(y^3+y^3\right)\)

\(=2y^3\)

Sửa đề \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

\(=8x^3+y^3-8x^3+y^3=2y^3\)

\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

\(=8x^3+y^3-8x^3+y^3\)

\(=2y^3\)

a)  \(A=x^2+2xy+y^2-4x-4y+1\)

\(=\left(x+y\right)^2-4\left(x+y\right)+1\)

\(=3^2-4.3+1=-2\)

b)  \(B=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)

\(=x^2+2x+y^2-2y-2xy+37\)

\(=\left(x-y\right)^2+2\left(x-y\right)+37\)

\(=7^2+2.7+37=100\)

c)  \(C=x^2+4y^2-2x+10+4xy-4y\)

\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)

\(=5^2-2.5+10=25\)

a) \(A=x^2+2xy+y^2-4x-4v+1\)

\(=\left(x+y\right)^2-4\left(x+y\right)+1\)

\(=3^2-4.3+1=-2\)

a) Ta có: \(\left(y+3\right)\left(y^2-3y+9\right)-\left(60-y^3\right)\)

\(=y^3+27-60+y^3\)

\(=2y^3-33\)

b) Ta có: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

\(=8x^3+y^3-8x^3+y^3\)

\(=2y^3\)