Toán Lớp 8: Phân tích đa thức thành nhân tử:
a. 12x3y – 24x^2y^2 + 12xy^3
b. x^2 – 6 x +xy – 6y
c. 2x^2+ 2xy – x – y
d. ax – 2x – a^2 +2a
e. x^3- 3x^2 + 3x -1
f. 3x^2 – 3y^2 – 12x – 12y
g. x^2 – 2xy – x^2+ 4y^2
h. x^2 + 2x + 1 – 16
i. x^2 – 4x + 4 – 25y^2
k. x^2 – 6xy + 9y^2 -25z^2
l. 81 – x^2 + 4xy – 4y^2
m.x^2 +6x –y^2 +9
n.x^2 – 2x – 4y^2 + 1
o. x^2 – 2x -3
p. x^2 + 4x -12
q. x^2 + x – 6
s. x^2 -5x -6
t. x^2 – 8 x – 9
u, x^2 + 3x – 18
v, x^2 – 8x +15
x, x^2 + 6x +8
z, x^2-7 x + 6
w, 3x^2 – 7x + 2
y, x^4 + 64
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Gửi b
$= 12xy( x^2 – 2xy + y^2)$
$=12xy(x-y)^2$
Áp dụng HĐT số 2: $(A-B)^2= A^2-2AB+B^2$
$=(x^2+xy)-(6x+6y)$
$=(x+y)(x+6)$
$=2x(x+y)-(x+y)$
$=(x+y)(2x-1)$
$=x(a-2)-a(a-2)$
$=(a-2)(x-a)$
$=(x-1)^3$
Áp dụng HĐT số 5:$(A-B)^3= A^3-3A^2B+3AB^2-B^3$
$=3(x^2-y^2)-12(x+y)$
$=3(x-y)(x+y)-12(x+y)$
$=(x+y)(3x-3y-12)$
$=3(x+y)(x-y-4)$
Áp dụng HĐT số 3: $A^2-B^2= (A-B)(A+B)$
$=-2xy+4y^2$
$=-2y(x-2y)$
$=(x+1)^2-4^2$
$=(x+1-4)(x+1+4)$
$=(x-3)(x+5)$
HĐT số 3: $A^2-B^2 = (A-B)(A+B)$
$=(x^2-4x+4)-(5y)^2$
$=(x-2)^2-(5y)^2$
$=(x-2-5y)(x-2+5y)$
HĐT số 3: $A^2-B^2=(A-B)(A+B)$
$=(x-3y)^2-(5z)^2$
$=(x-3y-5z)(x-3y+5z)$
$=9^2 – (x^2-4xy+4y^2)$
$=9^2-(x-2y)^2$
$=(9+x-2y)(9-x+2y)$
$=(x^2+6x+9)-y^2$
$=(x+3)^2-y^2$
$=(x+3-y)(x+3+y)$
$=(x^2-2x+1)-4y^2$
$=(x-1)^2-(2y)^2$
$=(x-1-2y)(x-1+2y)$
$= x^2+x-3x-3$
$=x(x+1)-3(x+1)$
$=(x+1)(x-3)$
$=x(x-2) +6(x-2)$
$=(x-2)(x+6)$
$= x^2-2x+3x-6$
$=x(x-2)+3(x-2)$
$=(x+3)(x-2)$
$= x^2+x-6x-6$
$=x(x+1)-6(x+1)$
$=(x+1)(x-6)$
$=x^2+x-9x-9$
$=x(x+1)-9(x+1)$
$=(x+1)(x-9)$
$= x^2 -3x+6x-18$
$=x(x-3)+6(x-3)$
$=(x-3)(x+6)$
$= x^2 -3x-5x+15$
$=(x-3)(x-5)$
$=x^2+2x+4x+8$
$=x(x+2)+4(x+2)$
$=(x+2)(x+4)$
$=x^2-x-6x+6$
$=(x-1)(x-6)$
$= 3x^2-6x-x+2$
$=3x(x-2)-(x-2)$
$=(x-2)(3x-1)$
$= x^4 +16x^2 + 64 -16x^2$
$=(x^2)^2 + 2.8.x^2 +8^2 -16x^2$
$=(x^2+8)^2 – (4x)^2$
$=(x^2+8-4x)(x^2+8+4x)$