\(=\left(-5a\right)^3+3.\left(-5a\right)^2+3.\left(-5a\right)+1\)

\(=\left(-5a+1\right)^3\)

a) `64-96a+48a^2-8a^3`

`=-(8a^3-48a^2+96a-64)`

`=-[(2a)^3 - 3.(2a)^2 .4 + 3.2a.4^2 - 4^3]`

`=-(2a-4)^3`

b) `-m^3n^6-8`

`=-(m^3n^6+8)`

`=-[(mn^2)^3+2^3]`

`=-(mn^2+2)(m^2n^4-2mn^2+4)`.

Lời giải:

a.

$3x^2+xy-4y^2=(3x^2-3xy)+(4xy-4y^2)=3x(x-y)+4y(x-y)=(x-y)(3x+4y)$

b.

$x^8-5x^4+4=(x^8-x^4)-(4x^4-4)$

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

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

$=(x-1)(x+1)(x^2+1)(x-\sqrt{2})(x+\sqrt{2})(x^2+2)$

c.

$x^3+3x^2+3x-7=(x^3+3x^2+3x+1)-8$

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

$=(x-1)(x^2+4x+7)$

a) \(3x^2+xy-4y^2=3x^2-3xy+4xy-4y^2\)

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

b)\(x^8-5x^4+4=x^8-x^4-4x^4+4\)

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

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

c)\(x^3+3x^2+3x-7=x^3+3x^2+3x+1-8\)

\(\left(x+1\right)^3-\sqrt{2}^3=\left(x+1-\sqrt[]{2}\right)\left(\left(x+1\right)^2+2\sqrt{2}x+2\right)\)

a: \(3x^2+xy-4y^2\)

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

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

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

b: \(x^8-5x^4+4\)

\(=x^8-x^4-4x^4+4\)

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

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

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

\(a,=\left(2x-y\right)^2\\ b,=9x^2\left(x-y\right)-4\left(x-y\right)=\left(3x-2\right)\left(3x+2\right)\left(x-y\right)\\ c,=x^2+2+3x^2-6=4x^2-4=4\left(x-1\right)\left(x+1\right)\)

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

b) \(25x^2-12x-13=25x\left(x-1\right)+13\left(x-1\right)=\left(x-1\right)\left(25x+13\right)\)

a) \(3x^2+2x-5\)

\(=2x^2+x^2+2x-5\)

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

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

\(=\left(\sqrt{2}.x+x+1\right)\left(\sqrt{2}.x-x-1\right)\)

a: \(7x-14y=7\left(x-2y\right)\)

b: \(4x^2-4x+1=\left(2x-1\right)^2\)

\(a.6x^3-9x^2=3x^2\left(2x-3\right)\\ b.20x^2y-12x^3=4x^2\left(5y-3x\right)\)

a) \(6x^3-9x^2=3x^2\left(2x-3\right)\)

b) \(20x^2y-12x^3=4x^2\left(5y-3x\right)\)

a: \(6x^3-9x^2=3x^2\left(2x-3\right)\)

b: \(20x^2y-12x^3=4x^2\left(5y-3x\right)\)

\(a,=ab\left(a+3\right)\\ b,=\left(x-1\right)^2\\ c,=x\left[\left(x-3\right)^2-y^2\right]=x\left(x-y-3\right)\left(x+y-3\right)\)

a: =(x-1)²