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Bài 1
\(x^3-4x^2+8x-8=\left(x^3-8\right)-4x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4-4x\right)=\left(x-2\right)\left(x^2-2x+4\right)\)
Bài 2
\(a^2+b^2-a^2b^2+ab-a-b\)
\(=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)\)
\(=a^2\left(1-b\right)\left(1+b\right)+\left(a+b\right)\left(b-1\right)\)
\(=-a^2\left(b-1\right)\left(b+1\right)+\left(a+b\right)\left(b-1\right)\)
\(=\left(b-1\right)\left[a+b-a^2\left(b+1\right)\right]\)
\(=\left(b-1\right)\left(a+b-a^2b-a^2\right)\)
\(=\left(b-1\right)\left[\left(a-a^2\right)+b\left(1-a^2\right)\right]\)
\(=\left(b-1\right)\left[a\left(1-a\right)+b\left(1-a\right)\left(1+a\right)\right]\)
\(=\left(b-1\right)\left(1-a\right)\left[a+b\left(1+a\right)\right]\)
\(=\left(b-1\right)\left(1-a\right)\left(a+b+ab\right)\)
Bài 3
\(3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y-z\right)\left(x+y+z\right)\)
Bài 4
\(5x\left(x-2\right)-3x^2\left(x-2\right)=x\left(x-2\right)\left(5-3x\right)\)
\(3x\left(x-5y\right)-2y\left(5y-x\right)=3x\left(x-5y\right)+2y\left(x-5y\right)=\left(3x+2y\right)\left(x-5y\right)\)
2/ (b4 - 4b2 + 4) - 9a2 = (b2 - 2)2 - 9a2 = (b2 - 2 + 3a)(b2 - 2 - 3a)
a) 6x4 - 9x3 = 3x3(2x - 3)
b) 5y10 + 15y6 = 5y6(y4 + 3)
c) x2 - 6xy + 9y2 = x2 - 6xy + (3y)2 = (x - 3y)2
e) x3 - 64 = x3 - 43 = (x - 4)(x2 + 4x + 16)
f) 125x3 + y6 = (5x)3 + (y2)3 = (5x + y2)(25x2 + 5y2 + y4)
g) 0,125(a + 1)3 - 1 = [0,5(a + 1)]3 - 13 = (0,5a + 0,5)3 - 13 = (0,5a + 0,5 - 1)[(0,5a + 0,5)2 + (0,5a + 0,5) + 1) = (0,5a - 0,5)(0,25a^2 + 0,5 a + 0,25 + 0,5a + 0,5 + 1) = (0,5a - 0,5)(0,25a2 + 1,75 + a)
h) 3x2 - 12y2 = 3(x2 - 4y2) = 3[x2 - (2y)2 ] = 3(x - 2y)(x + 2y)
A = xy + y - 2x - 2
= y( x + 1 ) - 2( x + 1 )
= ( x + 1 )( y - 2 )
B = x2 - 3x + xy - 3y
= x( x - 3 ) + y( x - 3 )
= ( x - 3 )( x + y )
C = 3x2 - 3xy - 5x + 5y
= 3x( x - y ) - 5( x - y )
= ( x - y )( 3x - 5 )
D = xy + 1 + x + y
= y( x + 1 ) + ( x + 1 )
= ( x + 1 )( y + 1 )
E = ax - bx + ab - x2
= ( ax - x2 ) + ( ab - bx )
= x( a - x ) + b( a - x )
= ( a - x )( x + b )
F = x2 + ab + ax + bx
= ( ax + x2 ) + ( ab + bx )
= x( a + x ) + b( a + x )
= ( a + x )( x + b )
G = a3 - a2x - ay + xy
= a2( a - x ) - y( a - x )
= ( a - x )( a2 - y )
Bonus : = ( a - x )[ a2 - ( √y )2 ]
= ( a - x )( a - √y )( a + √y )
H = 2xy + 3z + 6y + xz
= ( 6y + 2xy ) + ( 3z + xz )
= 2y( 3 + x ) + z( 3 + x )
= ( 3 + x )( 2y + z )
A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1
B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)
C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)
D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)
E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)
F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)
G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)
H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)
a) (x-2)^3-x(x+1)(x-1)+6x(x-3)=0
\(x^3-6x^2+12x-8-x\left(x^2-1\right)+6x\left(x-3\right)=0\)
\(x^3-6x^2+12x-8-x^3+x+6x^2-18x=0\)
\(-5x-8=0\)
\(x=-\frac{8}{5}\)
Mai mik làm mấy bài kia sau
a2 - ab + a - b = (a2 - ab) + (a - b) = a(a - b) + (a - b) = (a - b)(a + 1)
5y2 - 10yz + 5z2 = 5(y2 -2yz + z2) = 5(y - z)2
3x2 - 12y2 = 3(x2 - 4y2) = 3(x - 2y)(x + 2y)
ab - b + a2 - a = (ab + a2) - (a + b) = a(a + b) - (a + b) = (a + b)(a - 1)
x2 - x - 6 = x2 + 2x - 3x - 6 = x(x + 2) - 3(x + 2) = (x + 2)(x - 3)