Giúp e với ạ
a) x3 - 4x2 + 4x
= x(x2 - 4x + 4)
= x(x - 2)2
b) x2 - 3x + 2
= x2 - x - 2x + 2
= (x2 - x) + (2x - 2)
= x(x - 1) + 2(x - 1)
= (x + 2)(x - 1)
c) 8x3 + \(\dfrac{1}{27}\)
= \(\left(2x+\dfrac{1}{3}\right)\)\(\left(4x^2-\dfrac{2}{3}x+\dfrac{1}{9}\right)\)
d) 64x3 - \(\dfrac{1}{8}\)
= \(\left(4x+\dfrac{1}{2}\right)\left(16x^2-2x+\dfrac{1}{4}\right)\)
e) x2 - 4 + (x - 2)2
= (x + 2)(x - 2) - (x - 2)2
= (x - 2)[(x + 2) - (x - 2)]
= (x - 2)(x + 2 - x + 2)
= 4(x - 2)
f) x3 - 2x3 + x - xy2
= -x3 + x - xy2
= -x(x2 - 1 + y2)
g) x3 - 4x2 - 12x + 27
= (x3 + 27) - (4x2 + 12x)
= (x + 3)(x2 - 3x + 9) - 4x(x + 3)
= (x + 3)[(x2 - 3x + 9) - 4x]
= (x + 3)(x2 - 3x + 9 - 4x)
= (x + 3)(x2 - 7x + 9)
h) 2x - 2y - x2 + 2xy - y2
= (2x - 2y) - (x2 - 2xy + y2)
= 2(x - y) - (x - y)2
= (x - y)(2 - x + y)
i) 3x2 + 6x + 3 - 3y2
= 3(x2 + 2x + 1 - y2)
= 3[(x2 + 2x + 1) - y2]
= 3[(x + 1)2 - y2]
= 3( x + 1 - y)(x + 1 + y)
k) 25 - x2 - y2 + 2xy
= 25 - (x2 - 2xy + y2)
= 25 - (x - y)2
= (5 - x + y)(5 + x - y)
l) 3x - 3y - x2 + 2xy - y2
= (3x - 3y) - (x2 - 2xy + y2)
= 3(x - y) - (x - y)2
= (x - y)(3 - x + y)
m) x2 - y2 + 2x - 2y
= (x2 - y2) + (2x - 2y)
= (x - y)(x + y) + 2(x - y)
= (x - y)(x + y + 2)
n) x4 + 2x3 - 4x - 4
= (x4 - 4) + (2x3 - 4x)
= (x2 - 2)(x2 + 2) + 2x(x2 - 2)
= (x2 - 2)(x2 + 2 + 2x)
o) x2(1 - x2) - 4x - 4x2
= x2(1 - x)( 1 + x) - 4x(1 + x)
= x(1 + x)[x(1 - x) - 4x]
= x(x + 1)(x - x2 - 4)
p) x3 + y3 + z3 - 3xyz
= x3 + y3 + z3 - 3x2y + 3x2y - 3xy2 + 3xy2 - 3xyz
= [(x3 + 3x2y + 3xy2 + y3) + z3] - (3x2y + 3xy2 + 3xyz)
= [(x + y)3 + z3] - 3xy(x + y + z)
= (x + y + z)[(x + y)2 - (x + y)z + z2] - 3xy(x + y + z)
= (x + y + z)(x2 + 2xy + y2 - xz - yz + z2 - 3xy)
= (x + y + z)(x2 + y2 + z2 - xy - xz - yz)
q) (x - y)3 + (y - z)3 + (z - x)3
= [(x - y) + (y - z)][(x - y)2 - (x - y)(y - z) + (y - z)2] + (z - x)3
= (x - z)(x2 - 2xy + y2 - xy + xz - y2 + yz + y2 - 2yz + z2) - (x - z)3
= (x - z)(x2 + y2 + z2 - 3xy + xz - yz) - (x - z)3
= (x - z)[x2 + y2 + z2 - 3xy + xz - yz - (x - z)2]
= (x - z)(x2 + y2 - 3xy + xz - yz - x2 + 2xz - z2)
= (x - z)(y2 - 3xy + 3xz - yz)
= (x - z)[(y2 - yz) - (3xy - 3xz)]
= (x - z)[y(y - z) - 3x(y - z)
= (x - z)(y - 3x)(y - z)
Nhớ tik nha
