1. 5x² - 4x

= x(5x - 4)

2. 8x²(x - 3y) - 12x(x - 3y)

= (8x² - 12x)(x - 3y)

= 4x(2x - 3)(x - 3y)

3. 3(x - y) - 5x(y - x)

= 3(x - y) + 5x(x - y)

= (3 + 5x)(x - y)

a: =(16x+20)^2-(10x+10)^2

=(16x+20-10x-10)(16x+20+10x+10)

=(26x+30)(6x+10)

=4(13x+15)(3x+5)

b: =(x-y+4-2x-3y+1)(x-y+4+2x+3y-1)

=(-x-4y+5)(3x+2y+3)

c: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(x^2+2x+1-x^2+2x-1)(x^2+2x+1+x^2-2x+1)

=2(x^2+1)*4x

=8x(x^2+1)

$16(4x+5)^2-25(2x+2)^2$

$=[4(4x+5)]^2-[5(2x+2)]^2$

$=[4(4x+5)-5(2x+2)][4(4x+5)+5(2x+2)]$

$=(16x+20-10x-10)(16x+20+10x+10)$

$=(6x+10)(26x+30)$

$=4(3x+5)(13x+15)$

$(x-y+4)^2-(2x+3y-1)^2$

$=[(x-y+4)-(2x+3y-1)][(x-y+4)+(2x+3y-1)]$

$=(-x-4y+5)(3x+2y+3)$

Vậy:

$=-(x+4y-5)(3x+2y+3)$

$(x+1)^4-(x-1)^4$

$=[(x+1)^2]^2-[(x-1)^2]^2$

$=[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]$

$=[x^2+2x+1-(x^2-2x+1)][x^2+2x+1+x^2-2x+1]$

$=(4x)(2x^2+2)$

$=8x(x^2+1)$

d)

Câu này không phân tích được thành nhân tử với hệ số nguyên/rational theo các hằng đẳng thức thông thường: $x^6-y^5$

\(8x^4y+12x^2y^2+20x^3y^3\)

\(=4x^2y\left(2x^2+3y+5xy^2\right)\)

\(=x^2y\left(8x^2+12y+20xy^3\right)\)

a: =(2x-3y)^2-4(2x-3y)

=(2x-3y)(2x-3y-4)

b: =3x^2+21x-x-7

=(x+7)(3x-1)

c: =(3x-1)^4+2(3x-1)^2+1

=[(3x-1)^2+1]^2

d: =2x^3-2x^2-x^2+x+x-1

=(x-1)(2x^2-x+1)

sai đề thì sửa dùm mik nhé

giúp mik bài này với

CẦN GẤP

1 ) ( 2x - 1 ) ( 8x + 12 ) + x²( 2x - 1 ) + ( 1 - 2x ).( 2x - 3 )

= ( 2x - 1 ) . ( 8x + 12 ) + x² ( 2x - 1 ) - ( 2x - 1 ) . ( 2x - 3 )

= ( 2x - 1 ) . ( 8x + 12 + x² - 2x + 3 )

= ( 2x - 1 ) . ( x² + 6x + 15 )

2 ) 3x ( x - y ) - 2y ( y - x ) - 4x + 4y

= 3x ( x - y ) + 2y ( x - y ) - 4. ( x - y )

= ( x - y ) ( 3x + 2y  - 4 )

12x^2(2x - y) - 4xy(2x + y) = 4x(x- y)(y + 6x)

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

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