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a)\(x^4+64=x^4+16x^2+64-16x^2\)
\(=\left(x^2\right)^2+2.x^2.8+8^2-\left(4x\right)^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
b)\(4x^4+81=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2\right)^2+2.2x^2.9+9^2-\left(6x\right)^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
c)\(x^4y^4+64=x^4y^4+16\left(xy\right)^2+64-16\left(xy\right)^2\)
\(=\left[\left(xy\right)^2\right]^2+2.\left(xy\right)^2.8+8^2-\left(8xy\right)^2\)
\(=\left[\left(xy\right)^2+8\right]^2-\left(8xy\right)^2\)
\(=\left[\left(xy\right)^2+8-8xy\right]\left[\left(xy\right)^2+8+8xy\right]\)
a, x^2 -4+ (x-2)^2=(x-2)(x+2)+(x-2)^2=(x-2)(x+2+x-2)=(x-2)2x , b, x^3-2x^2+x-xy^2=x(x^2-2x+1-y^2)=x((x-1)^2-y^2)=x(x-1-y)(x-1+y) c,x^3-4x^2-4x^2-12x+27=(x^3+27)-(4x^2+12x)=(x+3)(x^2-3x+9)-4x(x+3)=(x+3)(x^2-7x+9) cách giải đó pn.......
a) x2 - 4 + (x - 2)2
\(=\left(x^2-4\right)+\left(x-2\right)^2\)
\(=\left(x^2-2^2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left[\left(x+2\right)+\left(x-2\right)\right]\)
\(=\left(x-2\right)\left(x+2+x-2\right)\)
\(=\left(x-2\right)2x\)
b) x3 - 2x2 + x - xy2
\(=x\left(x^2-2x+1-y^2\right)\)
\(=x\left[\left(x^2-2x+1\right)-y^2\right]\)
\(=x\left[\left(x-1\right)^2-y^2\right]\)
\(=x\left[\left(x-1-y\right)\left(x-1+y\right)\right]\)
\(=x\left(x-1-1\right)\left(x-1+y\right)\)
c) x3 - 4x2 - 12x + 27
\(=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x^3+3^3\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left[\left(x^2-3x+9\right)-4x\right]\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
a) \(x^2\left(x-3\right)+12-4x=x^2\left(x-3\right)-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-4\right)\)
\(=\left(x-3\right)\left(x^2-2^2\right)\)
\(=\left(x+3\right)\left(x-2\right)\left(x+2\right)\)
b)\(x^2-4+\left(x-2\right)^2=x^2-2^2+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2+x-2\right)\)
\(=\left(x-2\right)2x\)
c)\(x^3-4x^2-12x+27=x^3+3x^2-7x^2-21x+9x+27\)
\(=x^2\left(x+3\right)-7x\left(x+3\right)+9\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
a) => x2.(x-3)-4(x-3)=(x-3)(x2-4)=(x-3)(x-2)(x+2)
b) => (x+2)(x-2)+(x-2)2=(x-2)(x+2+x-2)=2x(x-2)
c) => x3+27-(4x2+12x)=(x+3)(x2-3x+3)-4x(x+3)=(x+3)(x2-3x+3-4x)=(x-3)(x2-7x+3)
(a - b)2 - (b - a)
= (a - b)(a - b) + (a - b).1
= (a - b + 1)(a - b)
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