\(=\left(4x-x-1\right)\left(4x+x+1\right)=\left(3x-1\right)\left(5x+1\right)\)

\(=\left(4x-x-1\right)\left(4x+x+1\right)=\left(3x-1\right)\left(5x+1\right)\)

=(3x-1)(5x+1)

\(a,x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\\ v,x^3-2x^2-x+2=\left(x^3-2x^2\right)-\left(x-2\right)=x^2\left(x-2\right)-\left(x-2\right)=\left(x-2\right)\left(x^2-1\right)=\left(x-1\right)\left(x+1\right)\left(x-2\right)\\ c,25-16x^2=\left(5-4x\right)\left(5+4x\right)\)

\(a,=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\\ b,=x^2\left(x-2\right)-\left(x-2\right)\\ =\left(x-2\right)\left(x^2-1\right)=\left(x-1\right)\left(x-2\right)\left(x+2\right)\\ c,=\left(5-4x\right)\left(5+4x\right)\)

c: =(5-4x)(5+4x)

Bạn thử xem lại đề câu d nhé.

a) Ta có: \(4x\left(2x-3y\right)-8y\left(3y-2x\right)\)

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

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

b) Ta có: \(4x^2-4xy+y^2-9z^2\)

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

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

c) Ta có: \(x^2y+yz+xy^2+xz\)

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

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

a: \(50x^5-8x^3\)

\(=2x^3\left(25x^2-4\right)\)

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

b: \(x^4-5x^2-4y^2+10y\)

\(=\left(x^2-2y\right)\left(x^2+2y\right)-5\left(x^2-2y\right)\)

\(=\left(x^2-2y\right)\left(x^2+2y-5\right)\)

c: \(36a^2+12a+1-b^2\)

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

\(=\left(6a+1-b\right)\left(6a+1+b\right)\)

d: \(x^3+y^3-xy^2-x^2y\)

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

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

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

e: Ta có: \(4x^2+4x-3\)

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

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

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

f: Ta có: \(9x^4+16x^2-4\)

\(=9x^4+18x^2-2x^2-4\)

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

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

g: Ta có: \(-6x^2+5xy+4y^2\)

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

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

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

h: Ta có: \(\left(x^2+4x\right)^2+8\left(x^2+4x\right)+15\)

\(=\left(x^2+4x\right)^2+3\left(x^2+4x\right)+5\left(x^2+4x\right)+15\)

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

\(=\left(x+1\right)\left(x+3\right)\left(x^2+4x+5\right)\)

 \(a,4x^2-1\)

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

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

\(b,25x^2-0,09\)

\(=\left(5x\right)^2-\left(0,3\right)^2\)

\(=\left(5x-0,3\right)\left(5x+0,3\right)\)

\(d,\left(x-y\right)^2-4\)

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

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

\(e,9-\left(x-y\right)^2\)

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

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

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

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

\(f,\left(x^2+4\right)^2-16x^2\)

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

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

\(=\left(x^2-2\cdot x\cdot2+2^2\right)\left(x^2+2\cdot x\cdot2+2^2\right)\)

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

#\(Toru\)

`#3107`

a)

`4x^2 - 1`

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

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

b)

`25x^2 - 0,09`

`= (5x)^2 - (0,3)^2`

`= (5x - 0,3)(5x + 0,3)`

d)

`(x - y)^2 - 4`

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

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

e)

`9 - (x - y)^2`

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

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

f)

`(x^2 + 4)^2 - 16x^2`

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

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

`= (x - 2)^2 * (x + 2)^2`

_____

Tất cả các câu trên bạn sử dụng hđt:

`A^2 - B^2 = (A - B)(A + B)`

\(#MaiChangLaAnhDau..\)

a.

$64x^3-16x^2+x=x(64x^2-16x+1)$

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

b.

$36-4xy+24y-x^2=(4y^2+24y+36)-(x^2+4xy+4y^2)$

$=(2y+6)^2-(x+2y)^2=(2y+6-x-2y)(2y+6+x+2y)$

$=(6-x)(x+4y+6)$

c.

$x^2+10x-2010.2020$

$=x^2+10x-(2015-5)(2015+5)

$=x^2+10x-(2015^2-5^2)$

$=(x^2+10x+5^2)-2015^2=(x+5)^2-2015^2$

$=(x+5-2015)(x+5+2015)=(x-2010)(x+2020)$

d.

$25x^2-121+22y-y^2$

$=(5x)^2-(y^2-22y+11^2)$

$=(5x)^2-(y-11)^2=(5x-y+11)(5x+y-11)$

e.

$(x^2+2x)(x^2+2x-2)-3$

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

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

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

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

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

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

a: \(64x^3-16x^2+x\)

\(=x\left(64x^2-16x+1\right)\)

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

b: \(36-4xy+24y-x^2\)

\(=-\left(x-6\right)\left(x+6\right)-4y\left(x-6\right)\)

\(=\left(x-6\right)\left(-x-6-4y\right)\)

c: \(x^2+10x-2010\cdot2020\)

\(=x^2+2020x-2010x-2010\cdot2020\)

\(=x\left(x+2020\right)-2010\left(x+2020\right)\)

\(=\left(x+2020\right)\left(x-2010\right)\)

(2x + 1)² - 16x²

= (2x + 1)² - (4x)²

= (2x + 1 + 4x)(2x + 1 - 4x)

= (6x + 1)(1 - 2x)

= (2x +1)² - (4x)² = (2x + 1 - 4x).(2x + 1 + 4x) = (1 - 2x).(6x + 1)

a) (x + y)² - 2(x + y) + 1 

= (x + y)² - 2.1.(x + y) + 1

= (x + y - 1)²

b) x³ + 1 - x² - x

= (x³ - x²) - (x - 1) 

= x²(x - 1) - (x - 1)

= (x² - 1)(x - 1) = (x - 1)(x + 1)(x - 1) = (x - 1)²(x + 1) 

c) 27x³ - 0,001 

= \(\left(3x\right)^3-\frac{1}{1000}=\left(3x\right)^3-\left(\frac{1}{10}\right)^3=\left(3x-\frac{1}{10}\right)\left(9x^2+\frac{3}{10}x+\frac{1}{100}\right)\)

d) 125x³ - 1 =(5x)³ - 1 = (5x - 1)(25x² + 5x + 1) 

e) (x² + 4)² - 16x² 

= (x² + 4)² - (4x)²

= (x² - 4x + 4)(x² + 4x + 4) 

= (x - 2)²(x + 2)²

= [(x - 2)(x + 2)]²

a.\(\left(x+y\right)^2-2\left(x+y\right)+1\)

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

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

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

b.\(x^3+1-x^2-x\)

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

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

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

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

c.\(27x^3-0,001\)

\(=27x^3-\frac{1}{1000}\)

\(=\left(3x\right)^3-\left(\frac{1}{10}\right)^3\)

\(=\left(3x-\frac{1}{10}\right)\left(9x^2+0,3x+\frac{1}{100}\right)\)

d,\(125x^3-1\)

\(=\left(5x\right)^3-1^3\)

\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)

e.\(\left(x^2+4\right)^2-16x^2\)

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

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

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

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

a) \(4x^2-1\)

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

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

b) \(x^2-3y^2\)

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

\(=\left(x-y\sqrt{3}\right)\left(x+y\sqrt{3}\right)\)

c) \(9x^2-\dfrac{1}{4}\)

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

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

d) \(\left(x-y\right)^2-4\)

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

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

e) \(9-\left(x-y\right)^2\)

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

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

f) \(\left(x^2+4\right)^2-16x^2\)

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

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

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