\(x^3+9x^2+27x+2027\)
\(=x^3+3\cdot x^2\cdot3+3\cdot x\cdot3^2+3^3+2000\)
\(=\left(x+3\right)^3+2000=\left(-23+3\right)^3+2000\)
=-8000+2000=-6000
\(16x^2-8xy+y^2-21\)
\(=\left(4x-y\right)^2-21\)
\(=\left(y+1-y\right)^2-21=1-21=-20\)
\(27x^3-27x^2y+9xy^2-y^3-121\)
\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot y+3\cdot3x\cdot y^2-y^3-121\)
\(=\left(3x-y\right)^3-121=\left(y+7-y\right)^3-121=7^3-121\)
=343-121=222
`A = x^3 +9x^2+27x+2027`
`= x^3 + 3 . x^2 . 3 + 3 . x . 3^3 + 3^3 + 2000`
`= (x+3)^3 + 2000`
Thay `x = -23`, ta được:
`A = (-23+3)^3 + 2000 = -8000 + 2000 = -6000`
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`B = 16x^2-8xy+y^2-21 `
`= (4x)^2 - 2 . 4x + y + y^2 - 21`
`= (4x - y)^2 - 21`
Nếu `4x = y +1`
`<=> 4x - y = 1` thì:
`B = 1^2 - 21 = 1 - 21 = -20`
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`C=27x^3 -27x^2y+9xy^2-y^3-121`
`= (3x)^3 - 3 . (3x^2) y + 3 . 3x . y^3 - y^3 - 121`
`= (3x - y)^3 - 121`
Nếu `3x = 7+y`
`<=> 3x - y = 7` thì:
`C = 7^3 - 121 = 222`
