x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)

k mk nha

bạn ơi bạn chưa bớt 2x^2 kìa

ngu dốt

x⁵-x⁴-1=x⁵-x³-x²-x⁴+x²+x+x³-x-1

=x².(x³-x-1)-x.(x³-x-1)+(x³-x-1)

=(x³-x-1)(x²-x+1)

x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)

k mk nha

mik chịu

\(x^8+x^4+1\)

\(=x^4.\left(x^4+1\right)+\left(x^4+1\right)-x^4\)

\(=\left(x^4+1\right).\left(x^4+1\right)-\left(x^2\right)^2\)

\(=\left(x^4+1\right)^2-\left(x^2\right)^2\)

\(=\left(x^4+1-x^2\right).\left(x^4+1+x^2\right)\)

x⁸ + x⁴ + 1

= x⁸ + 2x⁴ + 1 - x⁴

= (x⁴ + 1)² - x⁴

= (x⁴ + 1)² - (x²)²

= (x⁴ + 1 + x²)(x⁴ + 1 - x²)

= (x⁴ + x² + 1)(x⁴ - x² + 1)

\(a,=\left(5x^3+10x\right)+\left(x^4-4\right)\\ =5x\left(x^2+2\right)+\left(x^2+2\right)\left(x^2-2\right)\\ =\left(x^2+2\right)\left(x^2+5x-2\right)\\ b,=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\\ =\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\\ =\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\\ =\left(x+y+z\right)\left(x^2+2xy+y-xz-yz+z^2-3xy\right)\\ =\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

\(c,=\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\\ d,=\left(x^7+x^6+x^5\right)-\left(x^6+x^5+x^4\right)+\left(x^4+x^3+x^2\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\\ e,=\left(x^{10}+x^9+x^8\right)-\left(x^9+x^8+x^7\right)+\left(x^7+x^6+x^5\right)-\left(x^6+x^5+x^4\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^{10}-x^7+x^5-x^4+x^3-x+1\right)\)

a: =x^4+2x^2+5x^3+10x-2x^2-4

=(x^2+2)(x^2+5x-2)

b; =(x+y)^3+z^3-3xy(x+y)-3xyz

=(x+y+z)*(x^2+2xy+y^2-xz-yz+z^2)-3xy(x+y+z)

=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)

c: =x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1

=(x^2+x+1)(x^6-x^5+x^3-x^2+1)

x³-3x²-4=

\(=x^4+2x^2+1-\left(\sqrt{2}x\right)^2\)

\(=\left(x^2+1\right)^2-\left(\sqrt{2}x\right)^2\)

\(=\left(x^2+1-\sqrt{2}x\right)\left(x^2+1+\sqrt{2}x\right)\)

\(x^4+1\)

\(=x^4+2x^2+1-2x^2\)

\(=\left(x^2+1\right)^2-\left(x\sqrt{2}\right)^2\)

\(=\left(x^2-x\sqrt{2}+1\right)\left(x^2+x\sqrt{2}+1\right)\)

bằng sau này bn nhá

64x^4+81

=64x^4+144x^2+81-144x^2

=(8x^2+9)^2-(12x)^2

=(8x^2-12x+9)(8x^2+12x+9)

x^8+4y^4

=x^8+4x^4y^2+4y^4-4x^4y^2

=(x^4+2y^2)^2-(2x^2y)^2

=(x^4-2x^2y+2y^2)(x^4+2x^2y+2y^2)

x^8+x^7+1

=x^8+x^7+x^6-x^6+1

=x^6(x^2+x+1)-(x^6-1)

=(x^2+x+1)*x^6-(x-1)(x+1)(x^2+x+1)(x^2-x+1)

=(x^2+x+1)[x^6-(x^2-1)(x^2-x+1)]

=(x^2+x+1)(x^6-x^4+x^2-x^2+x^2-x+1)

=(x^2+x+1)(x^6-x^4+x^2-x+1)

\(x^4+81\)

\(=x^4+3^4\)

\(=\left(x^2+3^2\right)^2-2x^23^2\)

\(=\left(x^2+\sqrt{2}x3+3^2\right)\left(x^2-\sqrt{2}x3+3^2\right)\)

nguồn gg

\(x^4+81\)

\(=x^4+18x^2+81-18x^2\)

\(=\left(x^2+9\right)^2-18x^2\)

\(=\left(x^2-3\sqrt{2}x+9\right)\left(x^2+3\sqrt{2}x+9\right)\)