Đặt nhân tử chung
a) y^4 - y^3 + y^2 - y
b) 64m^3 + 8y^3
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
MH
28 tháng 10 2021
a) \(4\left(2-x\right)^2+xy-2y\)
\(=4\left(x-2\right)^2+\left(xy-2y\right)\)
\(=4\left(x-2\right)\left(x-2\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(4x-8\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(4x-8+x-2\right)\)
\(=\left(x-2\right)\left(5x-10\right)\)
\(=5\left(x-2\right)^2\)
28 tháng 10 2021
a, \(=4\left(x-2\right)^2+y\left(x-2\right)=\left(x-2\right)\left(4x-8+y\right)\)
b, \(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-xy+y^2-y^2\right]=\left(x-y\right)\left(x^3-2x^2y+xy^2-xy\right)=x\left(x-y\right)\left(x^2-2xy+y^2-y\right)\)
c, \(=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\)
d, không phân tích được
14 tháng 10 2020
11) \(3x\left(x-1\right)+5\left(1-x\right)=\left(3x-5\right)\left(x-1\right)\)
12) \(2\left(2x-1\right)+3\left(1-2x\right)=1-2x\)
13) \(10x\left(x-y\right)-8y\left(y-x\right)=2\left(x-y\right)\left(5x+4y\right)\)
14) \(3x\left(y+2\right)-3\left(y+2\right)=3\left(x-1\right)\left(y+2\right)\)
15) \(x^2-y^2-2x+2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right)\)
6 tháng 7 2023
\(a,\)
\(x^3y-y\)
\(=y\left(x^3-1\right)\)
\(=y\left[\left(x-1\right)\left(x^2+x+1\right)\right]\)
\(=y\left(x-1\right)\left(x^2+x+1\right)\)
\(b,\)
\(x^3y+y\)
\(=y\left(x^3+1\right)\)
\(=y\left[\left(x+1\right)\left(x^2-x+1\right)\right]\)
\(=y\left(x+1\right)\left(x^2-x+1\right)\)
\(c,\)
\(\left(x-y\right)^2-x\left(y-x\right)\)
\(=\left(x-y\right)^2+x\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+x\right)\)
\(=\left(x-y\right)\left(2x-y\right)\)
AH
Akai Haruma
Giáo viên
22 tháng 8 2023
Lời giải:
a.
$64x^2-24y^2=8(8x^2-3y^2)=8(\sqrt{8}x-\sqrt{3}y)(\sqrt{8}x+\sqrt{3}y)$
b.
$64x^3-27y^3=(4x)^3-(3y)^3=(4x-3y)(16x^2+12xy+9y^2)$
c.
$x^4-2x^3+x^2=(x^2-x)^2=[x(x-1)]^2=x^2(x-1)^2$
d.
$(x-y)^3+8y^3=(x-y)^3+(2y)^3=(x-y+2y)[(x-y)^2-2y(x-y)+(2y)^2]$
$=(x+y)(x^2-4xy+7y^2)$
H9
HT.Phong (9A5)
CTVHS
22 tháng 8 2023
a) \(64x^2-24y^2\)
\(=8\left(8x^2-3y^2\right)\)
b) \(64x^3-27y^3\)
\(=\left(4x\right)^3-\left(3y\right)^3\)
\(=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)
c) \(x^4-2x^3+x^2\)
\(=x^2\left(x^2-2x+1\right)\)
\(=x^2\left(x-1\right)^2\)
d) \(\left(x-y\right)^3+8y^3\)
\(=\left(x-y+2y\right)\left(x^2-2xy+y^2-2xy+2y^2+4y^2\right)\)
\(=\left(x+y\right)\left(x^2-4xy+7y^2\right)\)
5 tháng 9 2017
a) \(5x^2\)\(\left(x-2y\right)\)\(-\)\(15x\)\(\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=5x\left(x-2y\right)\left(x-3\right)\)
b) \(3\left(x-y\right)\)\(-\)\(5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
c) \(10x\left(x-y\right)\)\(-\)\(8y\left(y-x\right)\)
\(=\)\(10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(5x+4\right)\left(x-y\right)\)
d) \(x^2\)\(\left(x-5\right)\)\(+\)\(4\)\(\left(5-x\right)\)
\(=x^2\)\(\left(x-5\right)\)\(-\)\(4\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2-4\right)\)
\(=\left(x-5\right)\left(x-2\right)\left(x-2\right)\)
5 tháng 9 2017
a) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=\left(x-2y\right)\left(x-3\right)5x\)
b)\(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(3+5x\right)\left(x-y\right)\)
c)\(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(10x+8y\right)\left(x-y\right)\)
\(=2\left(5x+4y\right)\left(x-y\right)\)
d)\(x^2\left(x-5\right)+4\left(5-x\right)\)
\(=x^2\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x^2-4\right)\left(x-5\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-5\right)\)
7 tháng 9 2021
\(3,x\left(x-1\right)-y\left(1-x\right)=\left(x+y\right)\left(x-1\right)\\ 4,x^3+6x^2y+12xy^2+8y^3=\left(x+2y\right)^3\\ 5,x^2-2xy+y^2-xz+yz=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y-z\right)\left(x-y\right)\\ 6,x^2-y^2-x+y=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\\ 9,x^3+x^2-xy+xy+y^2+y^3\\ =x^2\left(x+1\right)+y^2\left(x+1\right)=\left(x^2+y^2\right)\left(x+1\right)\\ 10,x^2-6\left(x+3\right)-9\\ =x^2-6x-18-9\\ =x^2-6x-27=\left(x-9\right)\left(x+3\right)\)
7 tháng 9 2021
10: \(x^2-6\left(x+3\right)-9\)
\(=x^2-6x-18-9\)
\(=x^2-6x-27\)
\(=\left(x-9\right)\left(x+3\right)\)
24 tháng 8 2023
=(x-y-2y)[(x-y)^2+2y(x-y)+4y^2]
=(x-3y)(x^2-2xy+y^2+2xy-2y^2+4y^2)
=(x-3y)(x^2+3y^2)
H9
HT.Phong (9A5)
CTVHS
24 tháng 8 2023
\(\left(x-y\right)^3-8y^3\)
\(=\left(x-y\right)^3-\left(2y\right)^3\)
\(=\left[\left(x-y\right)-2y\right]\left[\left(x-y\right)^2+2y\left(x-y\right)+\left(2y\right)^2\right]\)
\(=\left(x-y-2y\right)\left(x^2-2xy+y^2+2xy-2y^2+4y^2\right)\)
\(=\left(x-3y\right)\left(x^2+3y^2\right)\)
\(a,y^4-y^3+y^2-y=y^3\left(y-1\right)+y\left(y-1\right)\)
\(=\left(y-1\right)\left(y^3+y\right)=y\left(y-1\right)\left(y^2+1\right)\)
\(b,64m^3+8y^3=8\left(8m^3+y^3\right)\)
\(=8\left[\left(2m\right)^3+y^3\right]=8\left(2m+y\right)\left(4m^2-2my+y^2\right)\)
a)
\(y^4-y^3+y^2-y\)= \(y\left(y^3-y^2+y-1\right)=y\left(y^2\left(y-1\right)+\left(y-1\right)\right)\)
= \(y\left(y-1\right)\left(y^2+1\right)\)
b) =8.(8m3+y3)