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Bài làm
a, \(2x^2\left(3x-5\right)=6x^3-10x^2\)
b, \(\left(12x^3y^2-18x^2y\right):2xy=\left(12x^3y^2:2xy\right)-\left(18x^2y:2xy\right)=6x^2y-9x\)
a.2x2-12x2+18x
=>2x(x2-6x+9)
=>2x(x-3)2
b.(x2+x)2+4x2+4x-12
=>x4+2x3+x2+4x2+4x-12
=>x4+2x3+5x2+4x-12
a) \(2x^3-12x^2+18x=2x\left(x^2+6x+9\right)=2x\left(x+3\right)^2\)
b) \(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)^2+6\left(x^2+x\right)-2\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)
\(=\left(x^2-x+2x-2\right)\left(x^2+x+6\right)\)
\(=\left[x\left(x-1\right)+2\left(x-1\right)\right]\left(x^2+x+6\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
b) \(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
d) \(x^{16}-1=\left(x^4-1\right)\left(x^4+1\right)=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\)
a) \(12x^3+8x^2-3x-2=4x^2\left(3x+2\right)-\left(3x+2\right)\)
\(=\left(3x+2\right)\left(4x^2-1\right)=\left(3x+2\right)\left(2x-1\right)\left(2x+1\right)\)
b) \(18x^3+27x^2-2x-3=9x^2\left(2x+3\right)-\left(2x+3\right)\)
\(=\left(2x+3\right)\left(9x^2-1\right)=\left(2x+3\right)\left(3x-1\right)\left(3x+1\right)\)
c) \(8x^3+4x^2-34x+15=4x^2\left(2x-3\right)+8x\left(2x-3\right)-5\left(2x-3\right)\)
\(=\left(2x-3\right)\left(4x^2+8x-5\right)=\left(2x-3\right)\left(2x-1\right)\left(2x+5\right)\)
a) \(2x^2\left(3x-5\right)=2x^2.3x-2x^2.5=6x^3-10x^2\)
b) \(\left(12x^3y+18x^2y\right):2xy\)\(=12x^3y:2xy+18x^2y:2xy\)
\(=6x^2+9x=3x\left(2x+3\right)\)
\(2x^3-12x^2+18x\)
\(=2x\left(x^2-6x+9\right)\)
\(=2x\left(x-3\right)^2\)
2x3-12x2+18x
=>2x(x2-6x+9)
=>2x(x-3)2