\(2x^3-2xy^2-8x^2+8xy\)

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

\(=2x\left[\left(x^2-y^2\right)-4\left(x-y\right)\right]\)

\(=2x\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]\)

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

2x^3 - 2xy^2 - 8x^2 + 8xy 

= 2x^2 ( x - y ) - 8x ( x - y ) 

= ( x - y ) ( 2x^2 - 8x ) 

= ( x - y ) 2x ( x - 4 ) 

20% dd

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\(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2\right)-8x\left(x-y\right)=2x\left(x-y\right)\left(x+y\right)-8x\left(x-y\right)=2x\left(x-y\right)\left(x+y-4\right)\)

\(2x^3-2xy^2-8x^2+8xy\)

\(=2x\left(x^2-y^2\right)-8x\left(x-y\right)\)

\(=2x\left(x+y\right)\left(x-y\right)-8x\left(x-y\right)\)

\(=\left[2x\left(x+y\right)-8x\right]\left(x-y\right)\)

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

Ta có:

D=2x2+3y2+4xy−8x−2y+18C=2x2+3y2+4xy−8x−2y+18

D=2(x2+2xy+y2)+y2−8x−2y+18C=2(x2+2xy+y2)+y2−8x−2y+18

D=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1C=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1

D=2(x+y−2)2+(y+3)2+1≥1C=2(x+y−2)2+(y+3)2+1≥1

Dấu "=" xảy ra ⇔x+y=2⇔x+y=2và y=−3y=−3

Hay x = 5 , y = -3

Đc chx bạn

\(A=2x^4+4x^3-7x^3-14x^2+8x^2+16x\)

\(=2x^2\left(x^2+2x\right)-7x\left(x^2+2x\right)+8\left(x^2+2x\right)\)

\(=\left(2x^2-7x+8\right)\left(x^2+2x\right)\)

\(=x\left(x+2\right)\left(2x^2-7x+8\right)\)

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

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

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

\(C=x\left(8y^2+8xy+2x^2-z^2\right)\)

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

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

\(=x\left(\sqrt{2}x+2\sqrt{2}y-z\right)\left(\sqrt{2}x+2\sqrt{2}y+z\right)\)

\(D=4a^4+10a^3+6a^2-6a^2-15a-9\)

\(=2a^2\left(2a^2+5a+3\right)-3\left(2a^2+5a+3\right)\)

\(=\left(2a^2-3\right)\left(2a^2+5a+3\right)\)

\(E=4a^3-ab^2+2ab-4a^2\)

\(=a\left(4a^2-b^2\right)-2a\left(2a-b\right)\)

\(=a\left(2a+b\right)\left(2a-b\right)-2a\left(2a-b\right)\)

\(=\left(2a-b\right)\left(2a^2+ab-2a\right)\)

\(F=5a^2-10a-4a+8\)

\(=5a\left(a-2\right)-4\left(a-2\right)\)

\(=\left(5a-4\right)\left(a-2\right)\)

\(G=a\left(2x+3y\right)-\left(2x+3y\right)\)

\(=\left(a-1\right)\left(2x+3y\right)\)

a>(8x^2y+10xy6^2-6xy):2xy=4xy+5y-3

b>(3x^2-4x).(2x-6)=6x^3-26x^2+24x

Lời giải:

$2x^3y+2xy^3+4x^2y^2-8xy$

$=2xy(x^2+y^2+2xy-4)$

$=2xy[(x^2+2xy+y^2)-4]$

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

P.s: lần sau bạn lưu ý ghi đầy đủ yêu cầu đề.