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a) \(\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left[\left(x+8\right)-\left(x-2\right)\right]^2\)
\(=\left(x+8-x+2\right)^2\)
\(=10^2\)
\(=2^2.5^2\)
b)\(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
c)\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
d)\(x^3+6x^2-13x-42=x^3-3x^2+9x^2-27x+14x-42\)
\(=x^2\left(x-3\right)+9x\left(x-3\right)+14\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+9x+14\right)\)
\(=\left(x-3\right)\left(x^2+2x+7x+14\right)\)
\(=\left(x-3\right)\left[x\left(x+2\right)+7\left(x+2\right)\right]\)
\(=\left(x-3\right)\left(x+2\right)\left(x+7\right)\)
\(x^3+6x^2-13x-42\)
\(x^3+6x^2-13x-42\)
\(=\left(x+7\right)\left(x-3\right)\left(x+2\right)\)
b, \(2x^3-x^2+3x+6\)
\(=2x^3+2x^2-3x^2-3x+6x+6\)
\(=2x^2\left(x+1\right)-3x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^2-3x+6\right)\)
a)\(x^3+x+2=x^3+1+x+1\)
\(=\left(x+1\right)\left(x^2-x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+2\right)\)
b)\(x^3+3x^2-4=x^3-1+3x^2-3\)
\(=\left(x-1\right)\left(x^2+x+1\right)+3\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+3\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left[x^2+x+1+3x+3\right]\)
\(=\left(x-1\right)\left(x+2\right)^2\)
\(x^4+6x^3+13x^2+12x+4\)
\(=x^4+2x^3+4x^3+8x^2+5x^2+10x+2x+4\)
\(=\left(x^4+2x^3\right)+\left(4x^3+8x^2\right)+\left(5x^2+10x\right)+\left(2x+4\right)\)
\(=x^3\left(x+2\right)+4x^2\left(x+2\right)+5x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x+2\right)\left(x^3+4x^2+5x+2\right)\)
\(=\left(x+2\right)\left(x^3+x^2+3x^2+3x+2x+2\right)\)
\(=\left(x+2\right)\left[x^2\left(x+1\right)+3x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x+2\right)\left(x+1\right)\left(x^2+3x+2\right)\)
\(=\left(x+2\right)\left(x+1\right)\left(x^2+x+2x+2\right)\)
\(=\left(x+2\right)\left(x+1\right)\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x+2\right)\left(x+1\right)\left(x+1\right)\left(x+2\right)\)
\(=\left(x+2\right)^2\left(x+1\right)^2\)
Cảm ơn bạn rất nhiều