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\(12y-9x^2+36-3x^2y\)
\(=\left(36-9x^2\right)-\left(3x^2y-12y\right)\)
\(=-9\left(x^2-4\right)-3y\left(x^2-4\right)\)
\(=\left(-3\right)\left(x-2\right)\left(x+2\right)\left(3+y\right)\)
1a) \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
b) \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
\(a,=-\left(x-1\right)^3\left[=\left(1-x\right)^3\right]\\ b,=\left(1-x\right)^3\)
=(x^3-y^3)-(x^2-y^2)
=(x-y)(x^2+xy+y^2)-(x+y)(x-y)
=(x-y)(x^2+xy+y^2-x-y)
\(x^3-3x^2y+3x^2y-y^3+y^2-x^2\)
\(=\left(x^3-y^3\right)+\left(-3x^2y+3x^2y\right)+\left(y^2-x^2\right)\)
\(=\left(x^3-y^3\right)-\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2-x-y\right)\)
\(x^4+3x^2+36\)
\(=\left(x^2\right)^2+2.x^2.6+6^2-9x^2\)
\(=\left(x^2+6\right)^2-\left(3x\right)^2=\left(x^2-3x+6\right)\left(x^2+3x+6\right)\)
\(2x^4-3x^3-7x^2+6x+8\)
\(=2x^4+2x^3-5x^3-5x^2-2x^2-2x+8x+8\)
\(=2x^3\left(x+1\right)-5x^2\left(x+1\right)-2x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^3-5x^2-2x+8\right)\)
\(=\left(x+1\right)\left[2x^2\left(x-2\right)-x\left(x-2\right)-4\left(x-2\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
Chúc bạn học tốt.
a/ \(4x^2-9\)
\(=\left(2x-3\right)\left(2x+3\right)\)
b/ \(3x\left(3x-2\right)+1\)
\(=9x^2-6x+1\)
\(=\left(3x-1\right)^2\)
\(a,=\left(2x-3\right)\left(2x+3\right)\)
\(b,=9x^2-6x+1=\left(3x-1\right)^2\)
\(3x^{2}+3x-36\)
\(=x^{2}+x-12\)
\(=x^{2}-3x+4x-12\)
\(=x(x-3)+4(x-3)\)
\(=(x+4)(x-3)\)
\(3x^2+3x-36=3\left(x^2+x-12\right)=3\left(x+4\right)\left(x-3\right)\)