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`(2x-y)(16x^4+8x^3y+4x^2y^2+2xy^3+y^4)`
`=(2x-y)[(2x)^4+(2x)^3y+(2x)^2y^2+2xy^3+y^4)`
`=(2x)^5-y^5`
`=32x^5-y^5`
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\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
\(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
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2x3y – 2xy3 – 4xy2 – 2xy
= 2xy(x2 - y2 - 2y - 1)
= 2xy[x2 - (y2 + 2y + 1)]
= 2xy[x2 - (y + 1)2 ]
= 2xy(x + y + 1)(x - y - 1)
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2 x 3 y – 2 x y 3 – 4 x y 2 – 2 x y = 2 x y ( x 2 – y 2 – 2 y – 1 ) = 2 x y [ x 2 – ( y 2 + 2 y + 1 ) ] = 2 x y [ x 2 – ( y + 1 ) 2 ]
= 2xy(x – y – 1)(x + y + 1)
Đáp án cần chọn là: A
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\(x^4-y^4+2x^3y-2xy^3\)
\(=\left(x^2+y^2\right)\left(x^2-y^2\right)+2xy\left(x^2-y^2\right)\)
\(=\left(x^2-y^2\right)\left(x^2+y^2+2xy\right)\)
\(=\left(x-y\right)\left(x+y\right)\left(x+y\right)^2\)
\(=\left(x-y\right)\left(x+y\right)^3\)
\(x^4-y^4+2x^3y-2xy^3\\ =\left(x^2\right)^2-\left(y^2\right)^2+2xy\left(x^2-y^2\right)\\ =\left(x^2-y^2\right)\left(x^2+y^2\right)+2xy\left(x^2-y^2\right)\\ =\left(x^2-y^2\right)\left(x^2+y^2+2xy\right)\\ =\left(x-y\right)\left(x+y\right)\left(x+y\right)^2\\ =\left(x-y\right)\left(x+y\right)^3\)
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Ta có
(A):
16 x 4 ( x – y ) – x + y = 16 x 4 ( x – y ) – ( x – y ) = ( 16 x 4 – 1 ) ( x – y ) = [ ( 2 x ) 4 – 1 ] ( x – y ) = [ ( 2 x ) 2 – 1 ] [ ( 2 x ) 2 + 1 ] ( x – y ) = ( 2 x – 1 ) ( 2 x + 1 ) ( 4 x 2 + 1 ) ( x – y )
Nên (A) sai
Và (B):
2 x 3 y – 2 x y 3 – 4 x y 2 – 2 x y = 2 x y ( x 2 – y 2 – 2 y – 1 ) = 2 x y [ x 2 – ( y 2 + 2 y + 1 ) ] = 2 x y [ x 2 – ( y + 1 ) 2 ] = 2 x y ( x – y – 1 ) ( x + y + 1 ) .
Nên (B) sai.
Vậy cả (A) và (B) đều sai.
Đáp án cần chọn là: C
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`x^2 -4x+4-y^2`
`=(x^2 -4x+4)-y^2`
`=(x-2)^2 -y^2`
`=(x-2-y)(x-2+y)`
`x^2+2xy+y^2-x-y`
`=(x^2+2xy+y^2) -(x+y)`
`=(x+y)^2 -(x+y)`
`=(x+y)(x+y-1)`
`x^2-2xy+y^2-9`
`=(x^2-2xy+y^2)-3^2`
`=(x-y)^2-3^3`
`=(x-y-3)(x-y+3)`
Tách ra đi cậu.
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\(a,=12x^2+18x-12x^2+x+1=19x+1\\ b,=4x^3y^4-3xy^2-\dfrac{3}{2}x\)
ai giúp mk với! ko hỉu này lắm ạ!
= 2xy(x2-2xy+y2)
= 2xy (x+y)2