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7 tháng 8 2021

\(=\left[\left(x+y\right)-1\right]^2\)

Bài 1: 

a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)

\(=\left(2x+1\right)\left(3-2x+5\right)\)

\(=\left(2x+1\right)\left(8-2x\right)\)

\(=2\left(4-x\right)\left(2x+1\right)\)

b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)

\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)

\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)

\(=\left(3x-2\right)\left(3x-6\right)\)

\(=3\left(3x-2\right)\left(x-2\right)\)

Bài 2: 

a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)

\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)

\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)

\(=\left(a-b\right)\left(2a-4b\right)\)

\(=2\left(a-b\right)\left(a-2b\right)\)

f: Ta có: \(x^2-6xy+9y^2+4x-12y\)

\(=\left(x-3y\right)^2+4\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-3y+4\right)\)

25 tháng 11 2021

a)\(3xy-6y=3y\left(x-2\right)\)

b)\(x\left(x+y\right)+2x+2y=x\left(x+y\right)+\left(2x+2y\right)=x\left(x+y\right)+2\left(x+y\right)=\left(x+y\right)\left(x+2\right)\)

c)\(y^2-81=y^2-9^2=\left(y-9\right)\left(y+9\right)\)

a)`3xy-6y`

`=3y(x-2)`

b)`x(x+y)+2x+2y`

`=x(x+y)+2(x+y)`

`=(x+y)(x+2)`

c)`y^2 -81`

`=y^2-9^2`

`=(y-9)(y+9)`

a: \(=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)

b: \(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)

\(=\left(x^2y^2-9\right)\left(x^2y^2-7\right)\)

\(=\left(xy-3\right)\left(xy+3\right)\left(x^2y^2-7\right)\)

c: \(=x^2-8x+x-8\)

\(=x\left(x-8\right)+\left(x-8\right)\)

\(=\left(x-8\right)\left(x+1\right)\)

9 tháng 10 2023

\(a,xy+y^2-x-y\)

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

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

\(=\left(x+y\right)\left(y-1\right)\)

\(---\)

\(b,\left(x^2y^2-8\right)^2-1\)

\(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)

\(=\left[\left(xy\right)^2-9\right]\left(x^2y^2-7\right)\)

\(=\left(xy-3\right)\left(xy+3\right)\left(x^2y^2-7\right)\)

\(---\)

\(c,x^2-7x-8\)

\(=x^2+x-8x-8\)

\(=\left(x^2+x\right)-\left(8x+8\right)\)

\(=x\left(x+1\right)-8\left(x+1\right)\)

\(=\left(x+1\right)\left(x-8\right)\)

\(Toru\)

Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

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

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

3 tháng 8 2021

`(x+y)^3-(x-y)^3`

`=(x+y-x+y)[(x+y)^2+(x+y)(x-y)+(x-y)^2]`

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

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

AH
Akai Haruma
Giáo viên
27 tháng 11 2023

Lời giải:

a. $xy(x+y)-y(x+y)^2+y^2(x-y)$

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

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

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

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

$=y^2(-2y)=-2y^3$

b.

$x(x+y)^2-y(x+y)^2+xy-x^2$

$=[x(x+y)^2-y(x+y)^2]-(x^2-xy)$

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

$=(x-y)[(x+y)^2-x]=(x-y)(x^2+2xy+y^2-x)$

27 tháng 11 2023

a: \(xy\left(x+y\right)-y\left(x+y\right)^2+y^2\left(x-y\right)\)

\(=\left(x+y\right)\left[xy-y\left(x+y\right)\right]+y^2\left(x-y\right)\)

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

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

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

b: \(x\left(x+y\right)^2-y\left(x+y\right)^2+xy-x^2\)

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

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

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

5 tháng 8 2021
NV
10 tháng 1 2022

Kiểm tra lại \(x^2-2y+y^2...\) hay \(x^2-2xy+y^2...\)

16 tháng 11 2021

a) \(36a^4-y^2=\left(6a^2-y\right)\left(6a^2+y\right)\)

b) \(6x^2+x-2=2x\left(3x+2\right)-1\left(3x+2\right)=\left(3x+2\right)\left(2x-1\right)\)

16 tháng 11 2021

paylak về r hả iem =))