x^6(2*x-3)^2

\(9x^6-12x^7+4x^8\)

\(=x^6\left(4x^2-12x+9\right)\)

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

hk

tốt

a: \(x^3-2x+4\)

\(=x^3+2x^2-2x^2-4x+2x+4\)

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

b: \(x^3-4x^2+12x-27\)

\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2-x+9\right)\)

c: \(x^3+2x^2+2x+1\)

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

\(=\left(x+1\right)\left(x^2+x+1\right)\)

cái này có những biểu thức ko dùng được hđt hoặc đặt nhân tử chung =))) anh nghĩ đề em nên thay chữ và thành hoặc 

1, \(15x^2+10xy=5x\left(3x+2y\right)\)

2, \(24x-18y+30=6\left(4x-3y+5\right)\)

3, \(2x\left(y-2009\right)+5y\left(y-2009\right)=\left(y-2009\right)\left(2x+5y\right)\)

4, \(35x\left(y-8\right)-14y\left(8-y\right)=\left(y-8\right)\left(35x+14y\right)=7\left(5x+2y\right)\left(y-8\right)\)

5, \(x^2+14x+49=x^2+2.7x+7^2=\left(x+7\right)^2\)

6, \(9x^2-4=\left(3x-2\right)\left(3x+2\right)\)

Trả lời:

1, 15x² + 10xy = 5x ( 3x + 2y )

2, 24x - 18y + 30 = 6 ( 4x - 3y + 5 )

3, 2x ( y - 2009 ) + 5y ( y - 2009 ) = ( y - 2009 )( 2x + 5y )

4, 35x ( y - 8 ) - 14y ( 8 - y ) = 35x ( y - 8 ) + 14y ( y - 8 ) = ( y - 8 )( 35x + 14y ) = 7 ( y - 8 )( 5x + 2y )

5, x² + 14x + 49 = ( x + 7 )² 

6, 9x² - 4 = ( 3x - 2 )( 3x + 2 )

\(27y^3-9y^2+y-\frac{1}{27}\)

\(=\left(3y\right)^3-3.\left(3y\right)^2.\frac{1}{3}+3.3y.\left(\frac{1}{3}\right)^2-\left(\frac{1}{3}\right)^3\)

\(=\left(3y-\frac{1}{3}\right)^3\)

hk

tốt

7 Năm Rồi Ư!?

a: =4x^2+8x-3x-6

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

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

b: =3(3x^2-2x-1)

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

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

c: =2x^2-4x+x-2

=2x(x-2)+(x-2)

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

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

=3x(x+1)-2(x+1)

=(x+1)(3x-2)

e: =3x^2+9x+x+3

=3x(x+3)+(x+3)

=(x+3)(3x+1)

a) \(4x^2+5x-6\)

\(=4x^2+8x-3x-6\)

\(=\left(4x^2+8x\right)-\left(3x+6\right)\)

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

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

b) \(9x^2-6x-3\)

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

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

\(=3\left[3x\left(x-1\right)+\left(x-1\right)\right]\)

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

c) \(2x^2-3x-2\)

\(=2x^2-4x+x-2\)

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

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

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

d) \(3x^2+x-2\)

\(=3x^2+3x-2x-2\)

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

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

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

e) \(3x^2+10x+3\)

\(=3x^2+9x+x+3\)

\(=3x\left(x+3\right)+\left(x+3\right)\)

\(=\left(x+3\right)\left(3x+1\right)\)

a) \(x^{12}-y^4=\left(x^6\right)^2-\left(y^2\right)^2=\left(x^6-y^2\right)\left(x^6+y^2\right)=\left(x^3-y\right)\left(x^3+y\right)\left(x^6+y^2\right)\)

b) \(x^9+1=\left(x^3\right)^3+1=\left(x^3+1\right)\left(x^6-x^3+1\right)=\left(x+1\right)\left(x^6-x^3+1\right)^2\)

c) \(x^6-y^6=\left(x^2\right)^3-\left(y^2\right)^3=\left(x^2-y^2\right)\left(x^4-x^2y^2+y^4\right)=\left(x-y\right)\left(x+y\right)\left(x^4-x^2y^2+y^4\right)\)

d) \(x^6+1=\left(x^2\right)^3+1=\left(x^2+1\right)\left(x^4-x^2+1\right)\)

e) \(9x^6-12x^7+4x^8=x^6\left(9-12x+4x^2\right)=x^6\left(3-2x\right)^2\)

\(x^4-x^2+2x-1\)

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

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

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

hk

tốt

a) \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)

\(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)

\(=\left(3a+3b-2a+4b\right)\left(3a+3b+2a-4b\right)\)

\(=\left(a+7b\right)\left(5a-b\right)\)

b) \(9x^6-12x^7+4x^8\)

\(=x^6\left(9-12x+4x^2\right)\)

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

c) \(8x^6-27y^3\)

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

\(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)

d) \(\frac{1}{64}x^6-125y^3\)

\(=\left(\frac{1}{4}x^2\right)^3-\left(5y\right)^3\)

\(=\left(\frac{1}{4}x^2-5y\right)\left(\frac{1}{16}x^4+\frac{5}{6}xy+25y^2\right)\)

a, \(\left(4x+5\right)^2=\left(4x+5\right)\left(4x+5\right)=\left[\left(4x+5\right)4x\right]+\left[\left(4x+5\right)5\right]=4x^2+20x+25\)

b, \(\left(5x-2\right)^2=\left(5x-2\right)\left(5x-2\right)=\left[\left(5x-2\right)5x-\left(5x-2\right)2\right]=5x^2-10x+25\)

b, \(8^2-12x^2=\left(8^2-12x^2\right)\left(8^2+12x^2\right)\)

đúng ko :) 

@No name: Bị sai rồi nhé, a,b,c sai hết  :>

a) ( 4x + 5 )² 

= ( 4x )² + 2.4x.5 + 5² 

= 16x² + 40x + 25 

b) ( 5x - 2 )² 

= ( 5x )² - 2.5x.2 + 2² 

= 25x² - 20x + 4 

c) 8² - 12x² 

= 64 - 12x² 

= ( V8 - V12x )( V8 + V12x ) 

*V    là căn