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20 tháng 3 2016

b) a3 + b3 + c3 - 3abc

= ( a + b)3 - 3ab - 3ba + c - 3abc

= (a3 + 3a2b + 3ab2 + b3) + c3 - (3a2b + 3ab2 + 3ab) 

= (a + b)3 + c2 - 3ab(a + b + c)

= (a + b + c) [ (a  + b)2 - ( a + b )c + c^2 ]  - 3ab(a + b + c)

=  ( a + b + c ) ( a2 + b2 + 2ab - ac - bc + c2 -3ab )

=  ( a + b + c ) ( a2 + b2 + c2 - ab - ac - bc 

AH
Akai Haruma
Giáo viên
20 tháng 10 2020

Lời giải:

a)

$yz(y+z)+xz(z-x)-xy(x+y)=yz(y+z)+xz^2-x^2z-x^2y-xy^2$

$=yz(y+z)+x(z^2-y^2)-x^2(z+y)$

$=yz(y+z)+x(z-y)(z+y)-x^2(z+y)$

$=(y+z)(yz+xz-xy-x^2)$

$=(y+z)[z(x+y)-x(x+y)]=(y+z)(x+y)(z-x)$

b)

$2a^2b+4ab^2-a^2c+ac^2-4b^2c+2bc^2-4abc$

$=(2a^2b+4ab^2)-(a^2c+2abc)+(ac^2+2bc^2)-(4b^2c+2abc)$

$=2ab(a+2b)-ac(a+2b)+c^2(a+2b)-2bc(a+2b)$

$=(a+2b)(2ab-ac+c^2-2bc)$

$=(a+2b)[2b(a-c)-c(a-c)]$

$=(a+2b)(2b-c)(a-c)$

c)

$y(x-2z)^2+8xyz+x(y-2z)^2-2z(x+y)^2$

$=y[(y-2z)+(x-y)]^2+8xyz+x(y-2z)^2-2z(x+y)^2$

$=y(y-2z)^2+y(x-y)^2+2y(y-2z)(x-y)+8xyz+x(y-2z)^2-2z(x+y)^2$

$=y(y-2z)^2+y(x+y)^2-4xy^2+2y(y-2z)(x-y)+8xyz+x(y-2z)^2-2z(x+y)^2$

$=(y-2z)^2(x+y)+(x+y)^2(y-2z)-4xy(y-2z)+2y(y-2z)(x-y)$

$=(y-2z)^2(x+y)+(x+y)^2(y-2z)+2y(y-2z)(x-y-2x)$

$=(y-2z)^2(x+y)+(x+y)^2(y-2z)-2y(y-2z)(x+y)$

$=(x+y)(y-2z)[(y-2z)+(x+y)-2y]=(x+y)(y-2z)(x-2z)$

17 tháng 8 2020

Lời giải:

a)

$yz(y+z)+xz(z-x)-xy(x+y)=yz(y+z)+xz^2-x^2z-x^2y-xy^2$

$=yz(y+z)+x(z^2-y^2)-x^2(z+y)$

$=yz(y+z)+x(z-y)(z+y)-x^2(z+y)$

$=(y+z)(yz+xz-xy-x^2)$

$=(y+z)[z(x+y)-x(x+y)]=(y+z)(x+y)(z-x)$

b)

$2a^2b+4ab^2-a^2c+ac^2-4b^2c+2bc^2-4abc$

$=(2a^2b+4ab^2)-(a^2c+2abc)+(ac^2+2bc^2)-(4b^2c+2abc)$

$=2ab(a+2b)-ac(a+2b)+c^2(a+2b)-2bc(a+2b)$

$=(a+2b)(2ab-ac+c^2-2bc)$

$=(a+2b)[2b(a-c)-c(a-c)]$

$=(a+2b)(2b-c)(a-c)$

c)

$y(x-2z)^2+8xyz+x(y-2z)^2-2z(x+y)^2$

$=y[(y-2z)+(x-y)]^2+8xyz+x(y-2z)^2-2z(x+y)^2$

$=y(y-2z)^2+y(x-y)^2+2y(y-2z)(x-y)+8xyz+x(y-2z)^2-2z(x+y)^2$

$=y(y-2z)^2+y(x+y)^2-4xy^2+2y(y-2z)(x-y)+8xyz+x(y-2z)^2-2z(x+y)^2$

$=(y-2z)^2(x+y)+(x+y)^2(y-2z)-4xy(y-2z)+2y(y-2z)(x-y)$

$=(y-2z)^2(x+y)+(x+y)^2(y-2z)+2y(y-2z)(x-y-2x)$

$=(y-2z)^2(x+y)+(x+y)^2(y-2z)-2y(y-2z)(x+y)$

$=(x+y)(y-2z)[(y-2z)+(x+y)-2y]=(x+y)(y-2z)(x-2z)$

13 tháng 8 2018

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20 tháng 8 2015

bạn nên viết ra 2 câu 1 bài

2 tháng 9 2018

\(yz\left(y+z\right)+zx\left(z-x\right)-xy\left(x+y\right)\)

\(=yz\left(y+z\right)+zx\left(z-x\right)-xy\left[\left(y+z\right)-\left(z-x\right)\right]\)

\(=yz\left(y+z\right)+zx\left(z-x\right)-xy\left(y+z\right)+xy\left(z-x\right)\)

\(=y\left(y+z\right)\left(z-x\right)+x\left(z-x\right)\left(z-y\right)\)

\(=\left(z-x\right)\left(yz-xy+xz-xy\right)\)

7 tháng 7 2019

2) Để sau đi (em chưa nghĩ ra)

3) \(A=\left(x+y\right)\left(x^2-y^2\right)+\left(y+z\right)\left(y^2-z^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)

\(=\left(x+y\right)^2\left(x-y\right)+\left(y+z\right)^2\left(y-z\right)+\left(z+x\right)^2\left(z-x\right)\)

Đặt x - y = a; y - z = b => z - x = -(a+b)

\(A=\left(x+y\right)^2a+\left(y+z\right)^2b-\left(z+x\right)^2a-\left(z+x\right)^2b\)

\(=a\left[\left(x+y\right)^2-\left(z+x\right)^2\right]+b\left[\left(y+z\right)^2-\left(z+x\right)^2\right]\)

\(=\left(x-y\right)\left(x+y-z-x\right)\left(x+y+z+x\right)+\left(y-z\right)\left(y+z-z-x\right)\left(y+z+z+x\right)\)

\(=\left(x-y\right)\left(y-z\right)\left(2x+y+z\right)-\left(y-z\right)\left(x-y\right)\left(2z+x+y\right)\)

\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

Em tính sai sót chỗ nào thì thông cảm cho em ạ :>

3 tháng 11 2017

1)

=2(a4+b4+c4-4a2b2-4a2c2-4b2c2)

=2a4+2b4+2c4-4a2b2-4a2c2-4b2c2

=(a4-2a2b2+b4)+(a4-2a2c2+c4)+(b4-2b2c2+c4

`a, 4a^2 + 4a + 1 = (2a+1)^2`

`b, -3x^2 + 6xy - 3y^2`

` = -3(x-y)^2`

`c, (x+y)^2 - 2(x+y)z + z^2`

`= (x+y-z)^2`