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\(4x^2-25y^2\)
\(\left(2x\right)^2-\left(5y\right)^2\)
\(\left(2x-5y\right)\left(2x+5y\right)\)
chọn c
\(\left(3x-2y\right)^3+\left(y+2x\right)^3-\left(4x-5y\right)\left(16x^2+20xy+25y^2\right)\)
\(=27x^3-54x^2y+36xy^2-8y^3+y^3+6xy^2+12x^2y+8x^3-\left(64x^3-125y^3\right)\)
\(=35x^3-42x^2y+42xy^2-7y^3-64x^3+125y^3\)
\(=-29x^3-42x^2y+42xy^2+118y^3\)
a) \(39x-39y=39\left(x-y\right)\)
b) \(3x^2\left(x-3y\right)-5y\left(3y-x\right)=3x^2\left(x-3y\right)+5y\left(x-3y\right)\)
\(=\left(3x^2+5x\right)\left(x-3y\right)=x\left(3x+5\right)\left(x-3y\right)\)
c) \(16x^2+24xy+9y^2=\left(4x\right)^2+4x.3y.2+\left(3y\right)^2=\left(4x+3y\right)^2\)
d) \(25x^2-\frac{1}{25y^2}=\left(5x\right)^2-\left(\frac{1}{5y}\right)^2=\left(5x-\frac{1}{5y}\right)\left(5x+\frac{1}{5y}\right)\)
e) \(7x^2-7xy+5x-5y=7x\left(x-y\right)+5\left(x-y\right)=\left(x-y\right)\left(7x+5\right)\)
f) \(5x^2-45y^2-30y-5=5\left(x^2-9y^2-6y-1\right)=5\left[x^2-\left(9y^2+6y+1\right)\right]\)
\(=5\left[x^2-\left(3y+1\right)^2\right]=5\left(x-3y-1\right)\left(x+3y+1\right)\)
g) \(x^2+2x+1-y^2-4y-1=\left(x^2+2x+1\right)-\left(y^2+2y+1\right)\) ( Chắc đề vậy :v )
\(=\left(x+1\right)^2-\left(y+1\right)^2=\left(x+1-y-1\right)\left(x+1+y+1\right)=\left(x-y\right)\left(x+y+2\right)\)
h) \(4x^2+8x-5=4x^2-2x+10x-5=2x\left(2x-1\right)+5\left(2x-1\right)\)
\(=\left(2x-1\right)\left(2x+5\right)\)
16x\((\dfrac{-1}{4}x+\dfrac{4}{5}y)^2\)=16x\(\left(\dfrac{1}{16}x^2+\dfrac{-2}{5}xy+\dfrac{16}{25}y^2\right)=x^3-\dfrac{32}{5}x^2y+\dfrac{256}{25}xy^2\)
`#3107`
`a)`
`A=`\(3x^4 + \dfrac{1}3xyz - 3x^4 - \dfrac{4}3xyz + 2x^2y - 6z\)
`= (3x^4 - 3x^4) + (1/3xyz - 4/3xyz) + 2x^2y - 6z`
`= -xyz + 2x^2y - 6z`
Thay `x = 1; y = 3` và `z = 1/3` vào A
`A = -1*3*1/3 + 2*1^2*3 - 6*1/3`
`= -1 + 6 - 2`
`= 6 - 3`
`= 3`
Vậy, `A=3`
`b)`
`B=`\(4x^3 - \dfrac{2}7xyz - 4x^3 - \dfrac{4}3xyz + 4x^2y\)
`= (4x^3 - 4x^3) + (-2/7xyz - 4/3xyz) + 4x^2y`
`= -34/21 xyz + 4x^2y`
Thay `x = -1; y = 2` và `z = -1/2` vào B
`B = -34/21*(-1)*2*(-1/2) + 4*(-1)^2 * 2`
`= -34/21 + 8`
`= 134/21`
Vậy, `B = 134/21`
`c)`
`C=`\(4x^2 + \dfrac{1}2xyz - \dfrac{2}3xy^2z - 5x^2yz + \dfrac{3}4xyz\)
`= 4x^2 + (1/2xyz + 3/4xyz) - 2/3xy^2z - 5x^2yz `
`= 4x^2 + 5/4xyz - 2/3xy^2z - 5x^2yz`
Ta có:
`|y| = 2`
`=> y = +-2`
Thay `x = -1; y = 2` và `z = 1/2` vào C
`4*(-1)^2 + 5/4*(-1)*2*1/2 - 2/3*(-1)*2^2*1/2 - 5*(-1)^2*2*1/2`
`= 4 - 5/4 + 4/3 - 5`
`= -11/12`
Vậy, với `x = -1; y = 2; z = 1/2` thì `B = -11/12`
Thay `x = -1; y = -2; z = 1/2`
`B = 4*(-1)^2 + 5/4*(-1)*(-2)*1/2 - 2/3*(-1)*(-2)^2*1/2 - 5*(-1)^2*(-2)*1/2`
`= 4 + 5/4 + 4/3 + 5`
`= 139/12`
Vậy, với `x = -1; y = -2; z = 1/2` thì `B = 139/12.`