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\(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\begin{array}{l} a){\left( {ab - 1} \right)^2} + {\left( {a + b} \right)^2}\\ = {a^2}{b^2} - 2ab + 1 + {a^2} + 2ab + {b^2}\\ = {a^2}{b^2} + 1 + {a^2} + {b^2}\\ = {a^2}\left( {{b^2} + 1} \right) + \left( {{b^2} + 1} \right)\\ = \left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)\\ c){x^3} - 4{x^2} + 12x - 27\\ = {x^3} - 27 + \left( { - 4{x^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} - x + 9} \right)\\ b){x^3} + 2{x^2} + 2x + 1\\ = {x^3} + 2{x^2} + x + x + 1\\ = x\left( {{x^2} + 2x + 1} \right) + \left( {x + 1} \right)\\ = x{\left( {x + 1} \right)^2} + \left( {x + 1} \right)\\ = \left( {x + 1} \right)\left( {x\left( {x + 1} \right) + 1} \right)\\ = \left( {x + 1} \right)\left( {{x^2} + x + 1} \right)\\ d){x^4} - 2{x^3} + 2x - 1\\ = {x^4} - 2{x^3} + {x^2} - {x^2} + 2x - 1\\ = {x^2}\left( {{x^2} - 2x + 1} \right) - \left( {{x^2} - 2x + 1} \right)\\ = \left( {{x^2} - 2x + 1} \right)\left( {{x^2} - 1} \right)\\ = {\left( {x - 1} \right)^2}\left( {x - 1} \right)\left( {x + 1} \right)\\ = {\left( {x - 1} \right)^3}\left( {x + 1} \right)\\ e){x^4} + 2{x^3} + 2{x^2} + 2x + 1\\ = {x^4} + 2{x^3} + {x^2} + {x^2} + 2x + 1\\ = {x^2}\left( {{x^2} + 2x + 1} \right) + \left( {{x^2} + 2x + 1} \right)\\ = \left( {{x^2} + 2x + 1} \right)\left( {{x^2} + 1} \right)\\ = {\left( {x + 1} \right)^2}\left( {{x^2} + 1} \right) \end{array} |
a) 9x4+22+6x2+y2+2y
= (3x2)2+2.3x2.1+1+y2+2y+1+20
=(3x2+1)2 + (y+1)2+22+42
b)x4+4+4y2+5x2+4xy
=x4+5x2+4+4y2+4xy
=x4+4x2+4+4y2+4xy+x2
=(x2)2+2x22+22+(2y)2+2.2yx+x2
=(x2+2)2+(2y+x)2
c)z2+y2-6z+2y+10
=z2-6z+9+y2+2y+1
=z2-2.z.3+9+(y+1)2
=(z-3)2+(y+1)2
d)x2+4y2+m2+4mn+4xy+4n2
=x2+4xy+4y2+4n2+4mn+m2
=x2+2x2y+(2y)2+(2n)2+2.2nm+m2
=(x+2y)2+(2n+m)2
e)x2+y2-6nx+9n2+4my+4m2
=x2-6nx+9n2+y2+4my+4m2
=x2-2x3n+(3n)2+y2+2y2n+(2m)2
=(x-3n)2+(y+2m)2
f)4x2-4xm+2m2+4mn+4n2
=4n2-4xm+m2+4n2+4mn+m2
=(2n)2-2.2xm+m2+(2n)2+2.2nm+m2
=(2n-m)2+(2n+m)2
g) Ghi thiếu đề,đề đúng :
9x2-12xy+5y2+2y+1
=9x2-12xy+4y2+y2+2y+1
=(3x)2-2.3x2y+(2y)2+(y+1)2
=(3x-2y)2+(y+1)2