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a: \(x^3-2x+4\)
\(=x^3+2x^2-2x^2-4x+2x+4\)
\(=\left(x+2\right)\left(x^2-2x+2\right)\)
b: \(x^3-4x^2+12x-27\)
\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
c: \(x^3+2x^2+2x+1\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
a) \(\left(6x-1\right)^2-\left(3x+2\right)^2\)
\(=\left(6x-1+3x+2\right)\left(6x-1-3x-2\right)\)
\(=\left(9x+1\right)\left(3x-3\right)\)
\(=3\left(9x+1\right)\left(x-1\right)\)
b) \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left(6x+9\right)^2-\left(2x+2\right)^2\)
\(=\left(6x+9+2x+2\right)\left(6x+9-2x-2\right)\)
\(=\left(8x+11\right)\left(4x+7\right)\)
c) \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc\right)^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc+b^2+c^2-a^2\right)\left(2bc-b^2-c^2+a^2\right)\)
\(=-\left[\left(b+c\right)^2-a^2\right]\left(b^2-2bc+c^2-a^2\right)\)
\(=-\left(b+c-a\right)\left(b+c+a\right)\left[\left(b-c\right)^2-a^2\right]\)
\(=-\left(b+c-a\right)\left(b+c+a\right)\left(b-c-a\right)\left(b-c+a\right)\)
d) \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)
\(=\left(a^2+b^2-5+2ab+4\right)\left(a^2+b^2-5-2ab-4\right)\)
\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-3^2\right]\)
\(=\left(a+b+1\right)\left(a+b-1\right)\left(a-b-3\right)\left(a-b+3\right)\)
a) \(x^2+4x+3=\left(x^2+4x+4\right)-1=\left(x+2\right)^2-1^2=\left(x+1\right)\left(x+3\right)\) (mình sửa lại)
b) \(x^2+8x-9=\left(x^2+8x+16\right)-25=\left(x+4\right)^2-5^2=\left(x-1\right)\left(x+9\right)\)
c) \(3x^2+6x-9=3\left[\left(x^2+2x+1\right)-4\right]=3\left[\left(x+1\right)^2-2^2\right]=3\left(x-1\right)\left(x+3\right)\)
d) \(2x^2+x-3=2x^2-4x+2+5x-5=2\left(x^2-2x+1\right)+5\left(x-1\right)=2\left(x-1\right)^2+5\left(x-1\right)=\left(x-1\right)\left(2x+3\right)\)
a) \(9\left(2x-3\right)^2-4\left(x+1\right)^2\)
\(=\left[3\left(2x-3\right)-2\left(x+1\right)\right]\left[3\left(2x-3\right)+2\left(x+1\right)\right]\)
\(=\left(6x-9-2x-2\right)\left(6x-9+2x+2\right)\)
\(=\left(4x-11\right)\left(8x-7\right)\)
b) \(\left(x^2+4y^2-20\right)-16\left(xy-4\right)^2\)
\(=\left[\left(x^2-4xy+4y^2\right)-4\right]\left[\left(x^2+4xy+4y^2\right)-36\right]\)
\(=\left[\left(x-2y\right)^2-4\right]\left[\left(x+2y\right)^2-36\right]\)
\(=\left(x-2y-2\right)\left(x-2y+2\right)\left(x+2y-6\right)\left(x+2y+6\right)\)
a. 9 ( 2x - 3 )2 - 4 ( x + 1 )2
= [ 3 ( 2x - 3 ) ]2 - [ 2 ( x + 1 ) ]2
= [ 3 ( 2x - 3 ) - 2 ( x + 1 ) ] [ 3 ( 2x - 3 ) + 2 ( x + 1 ) ]
= ( 6x - 9 - 2x - 2 ) ( 6x - 9 + 2x + 2 )
= ( 4x - 11 ) ( 8x - 7 )
b. ( x2 + 4y2 - 20 )2 - 16 ( xy - 4 )2
= ( x2 + 4y2 - 20 )2 - [ 4 ( xy - 4 ) ]2
= [ x2 + 4y2 - 20 - 4 ( xy - 4 ) ] [ x2 + 4y2 - 20 + 4 ( xy - 4 ) ]
= ( x2 + 4y2 - 20 - 4xy + 16 ) ( x2 + 4y2 - 20 + 4xy - 16 )
= ( x2 + 4y2 - 4xy - 4 ) ( x2 + 4y2 + 4xy - 36 )
= [ ( x - 2y )2 - 22 ] [ ( x + 2y )2 - 62 ]
= ( x - 2y - 2 ) ( x - 2y + 2 ) ( x + 2y - 6 ) ( x + 2y + 6 )
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
a) \(\left(2x+5\right)^2\)\(-\left(x-9\right)^2\)
=\(\left(2x+5+x-9\right).\left(2x+5-x+9\right)\)
=\(\left(3x-4\right).\left(x+14\right)\)