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\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^6-x^4-9x^3+9x^2\)
\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
\(x^4-4x^3+8x^2-16x+16\)
\(=\left(x^2+4\right)^2-4x\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x^2+4-4x\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)
a) \(x^3-x^2-5x+125=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)=\left(x+5\right)\left(x^2-6x+25\right)\)
b) \(x^6-x^4-9x^3+9x^2=x^2\left(x^4-x^2-9x+9\right)=x^2\left[x^2\left(x-1\right)\left(x+1\right)-9\left(x-1\right)\right]=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
c) \(x^4-4x^3+8x^2-16x+16=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)=\left(x-2\right)\left(x^3-2x^2+4x+8\right)=\left(x-2\right)\left(x^2+4\right)\left(x-2\right)=\left(x-2\right)^2\left(x^2+4\right)\)
d) \(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left(a-b-2c\right)\left(a-b+2c\right)\)
tick cho mk vs nha
bài 1 : a, sai đề . đề đúng là x3 + x2 + 22 = x3 + 2x2- x2+ 4
= x2 ( x + 2 ) - ( x - 2 ) ( x + 2 ) = ( x + 2 ) ( x2 - x + 2 )
b, xy -y2 -x -y = ( xy -x ) + ( y2 - y ) = x ( y -1) + y ( y -1) = ( y -1 ) ( x +y )
Phân tích đa thức thành nhân tử
a. 3ab ( x+ y) - 6ab ( y+ x)
=( x + y) ( 3ab - 6ab )
= ( x +y ) ( - 3ab)
b.7a (x - 3)+a2(x2 - 9)
=7a( x- 3) + a2 ( x2 - 32)
=7a ( x - 3 ) + a2 ( x- 3 ) ( x+3 )
= ( x- 3) . 7a + a2 ( x + 3)
= ( x- 3) ( 7a +a2x + 3a2)
c. 34 (x + y) -x -y
= 34 ( x+ y) - ( x+y)
=(x +y ) ( 34 - 1) = 33 ( x+ y)
d. 25 x4 - 942
=( 5x2 )2 - 942
=( 5x2 - 94 ) ( 5x2+94)
e.( 5a - b )2 - ( 2a +3b)2
=( 5a -b -2a - 3b) (5a -b + 2a + 3b)
=(3a - 4b) (7a+ 2b)
k. 22 -3a - b2 +3b
=( 22 - b2 ) + ( -3a +3b)
=( 2-b) (2+b) + 3( -a +b)
1 ) \(x^3-2x^2y+xy^2-4x\)
\(=x\left(x^2-2xy+y^2-4\right)\)
\(=x\left[\left(x-y\right)^2-4\right]\)
\(=x\left(x-y-2\right)\left(x-y+2\right)\)
2 ) \(x^4-3x^2+2=x^4-2x^2-x^2+2=x^2\left(x^2-2\right)-\left(x^2-2\right)=\left(x^2-1\right)\left(x^2-2\right)=\left(x-1\right)\left(x+1\right)\left(x^2-2\right)\)
3 ) \(27ay^2-3a-3ab^2+6ab\)
\(=3a\left(9y^2-1-b^2+2b\right)\)
\(=3a\left[9y^2-\left(b^2-2b+1\right)\right]\)
\(=3a\left[9y^2-\left(b-1\right)^2\right]\)
\(=3a\left(3y-b+1\right)\left(3y+b-1\right)\)
4 ) \(y^3-3y^2-3y+1=\left(y^3+1\right)-3y\left(y+1\right)=\left(y+1\right)\left(y^2-y+1\right)-3y\left(y+1\right)\)
\(=\left(y+1\right)\left(y^2-y+1-3y\right)=\left(y+1\right)\left(y^2-4y+1\right)\)
a)x3+2x2y+xy2-4x
=x(x2 + 2xy +y2 -4)
=x[(x+y)2 -22 ]
=x(x+y-2)(x+y+2)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
\(x^4+4x^2-5\)
\(=\left(x^4+4x^2+4\right)-9\)
\(=\left(x^2+2\right)^2-9\)
\(=\left(x^2+2+3\right)\left(x^2+2-3\right)\)
\(=\left(x^2+5\right)\left(x^2-1\right)\)
nhanh lên hộ t đi :>>>>>>>>>>