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\(a,=3x^3y^3-3x^2y^3+3x^2y^4+3xy^5\\ b,=\left(2x^3-6x^2+10x-3x^2+9x-15\right):\left(x^2-3x+5\right)\\ =\left[2x\left(x^2-3x+5\right)-3\left(x^2-3x+5\right)\right]:\left(x^2-3x+5\right)\\ =2x-3\\ c,=\left[x^2\left(x-3\right)+\left(x-3\right)\right]:\left(x-3\right)=x^2+1\)
Ta có: \(\left(x^3-x^2y+xy^2-y^3\right)\left(x+y\right)\)
\(=\left[x^2\left(x-y\right)+y^2\left(x-y\right)\right]\left(x+y\right)\)
\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)
\(=x^4-y^4=2^4-\left(\dfrac{1}{2}\right)^4=16-\dfrac{1}{16}=\dfrac{255}{16}\)
`a)(x-1)(x^2+x+1)`
`=x^3+x^2+x-x^2-x-1`
`=x^3-1`
`b)(x^3+x^2y+xy^2+y^3)(x-y)`
`=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4`
`=x^4-y^4`
a) VT`=(x-1)(x^2+x+1)`
`=x^3 +x^2 +x -x^2-x-1 `
`=x^3-1=` VP.
b) VT `=(x^3+x^2y+xy^2+y^3)(x-y)`
`=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4`
`=x^4-y^4=` VP.
Ta có
B = x 3 + x 2 y – x y 2 – y 3 = x 2 ( x + y ) – y 2 ( x + y ) = ( x 2 – y 2 ) ( x + y ) = ( x – y ) ( x + y ) ( x + y ) = ( x – y ) ( x + y ) 2
Thay x = 3,25 ; y = 6,57 ta được
B = ( 3 , 25 – 6 , 75 ) ( 3 , 25 + 6 , 75 ) 2 = - 3 , 5 . 10 2 = - 350
Đáp án cần chọn là: B
a) \(=8-x^3-x\left(16-x^2\right)=8-x^3-16x+x^3=-16x+8\)
b) \(=\left[\left(x+3\right)\left(x^2-3x+9\right)\right]:\left(x^2-3x+9\right)-x+7\)
\(=x+3-x+7=10\)
D = ( x 3 + y 3 ) – x y ( x + y ) = ( x + y ) ( x 2 – x y + y 2 ) – x y ( x + y ) = ( x + y ) ( x 2 – x y + y 2 – x y ) = ( x + y ) [ x ( x – y ) – y ( x – y ) ] = ( x + y ) ( x – y ) 2
Vì x = y ó x – y = 0 nên D = ( x + y ) ( x – y ) 2 = 0
Đáp án cần chọn là: D
a)\(\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4=x^4-y^4\)
b) \(x\left(3x-18\right)-3\left(x-4\right)\left(x-2\right)+8=3x^2-18x-3x^2+18x-24+8=-16\)