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Ấn nhầm :v
a) \(4x^4-21x^2y^2+y^4\)
\(=\left(2x^2\right)^2-2\cdot2x^2\cdot y^2+y^2-25x^2y^2\)
\(=\left(2x^2-y^2\right)^2-\left(5xy\right)^2\)
\(=\left(2x^2-5xy-y^2\right)\left(2x^2+5xy-y^2\right)\)
b) \(x^5-5x^3+4x\)
\(=x^5-4x^3-x^3+4x\)
\(=x^3\left(x^2-4\right)-x\left(x^2-4\right)\)
\(=\left(x^2-4\right)\left(x^3-x\right)\)
\(=x\left(x-2\right)\left(x+2\right)\left(x^2-1\right)\)
\(=x\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)


\(=4x^4+21x^2y^2+y^4-25x^2y^2\)
\(\left(2x^2+y^2\right)-\left(5xy\right)^2\)
\(\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
=4x4+21x2y2+y4−25x2y2=4x4+21x2y2+y4−25x2y2
(2x2+y2)−(5xy)2(2x2+y2)−(5xy)2
(2x2+y2−5xy)(2x2+y2+5xy)


a: Ta có: \(10x^4-27x^3y-110x^2y^2-27xy^3+10y^4\)
\(=10x^4+20x^2y^2+10y^4-27xy\left(x^2+y^2\right)-130x^2y^2\)
\(=10\left(x^2+y^2\right)^2-27xy\left(x^2+y^2\right)-130x^2y^2\)
\(=10\left(x^2+y^2\right)^2-52xy\left(x^2+y^2\right)+25xy\left(x^2+y^2\right)-130x^2y^2\)
\(=2\left(x^2+y^2\right)\left(5x^2+5y^2-26xy\right)+5xy\left(5x^2+5y^2-26xy\right)\)
\(=\left(5x^2-26xy+5y^2\right)\left(2x^2+5xy+2y^2\right)\)
\(=\left(5x^2-25xy-xy+5y^2\right)\left(2x^2+4xy+xy+2y^2\right)\)
\(=\left\lbrack5x\left(x-5y\right)-y\left(x-5y\right)\right\rbrack\left\lbrack2x\left(x+2y\right)+y\left(x+2y\right)\right\rbrack\)
=(5x-y)(x-5y)(2x+y)(x+2y)
b: \(x^5-4x^4+3x^3+3x^2-4x+1\)
\(=x^5+x^4-5x^4-5x^3+8x^3+8x^2-5x^2-5x+x+1\)
\(=\left(x+1\right)\left(x^4-5x^3+8x^2-5x+1\right)\)
\(=\left(x+1\right)\left(x^4-x^3-4x^3+4x^2+4x^2-4x-x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(x^3-4x^2+4x-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left\lbrack\left(x^3-x^2\right)-3x^2+3x+x-1\right\rbrack\)
\(=\left(x+1\right)\left(x-1\right)\cdot\left(x-1\right)\left(x^2-3x+1\right)=\left(x+1\right)\left(x-1\right)^2\cdot\left(x^2-3x+1\right)\)


a)\(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)=x^2-\left(y+1\right)^2=\left(x-y-1\right)\left(x+y+1\right)\)
b)\(x^2.\left(1-x^2\right)-4+4x^2=x^2.\left(1-x^2\right)-4.\left(1-x^2\right)=\left(1-x^2\right).\left(x^2-2^2\right)\)\(=\left(1-x\right).\left(1+x\right).\left(x-2\right).\left(x+2\right)\)
Tham khảo nhé~
4x4 - 21 x2y2 + y4
= (4x4 + 4x2y2 + y4) - 25x2y2
= [(2x2)2 + 2x2 . 2 . y2 + (y2)2] - 25x2y2
= (2x2 + y2) - 25x2y2
= (2x2 + y2 - 5xy) (2x2 + y2 + 5xy)