a: 3x^2-12y^2

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

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

b: 5xy^2-10xyz+5xz^2

=5x(y^2-2yz+z^2)

=5x(y-z)^2

g: (a+b+c)^3-a^3-b^3-c^3

=(a+b+c-a)[(a+b+c)^2+a(a+b+c)+a^2]-(b+c)(b^2-bc+c^2)

=(b+c)[a^2+b^2+c^2+2ab+2ac+2bc+a^2+ab+ac+a^2-b^2+bc-c^2]

=(b+c)[3a^2+3ab+3bc+3ac]

=3(a+b)(b+c)(a+c)

\(a,=5xy\left(2x-y+3z\right)\\ b,=x^2\left(x-1\right)-4\left(x-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\\ c,=x\left(x^2-6x+9\right)=x\left(x-3\right)^2\)

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) \(3x^2+2x-5\)

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

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

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

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

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

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: \(x^8-5x^4+4\)

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

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

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

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

\(a,x^2-4xa+4a^2-81y^2=\left(x-2a\right)^2-\left(9y\right)^2=\left(x-2a-9y\right)\left(x-2a+9y\right)\\ b,3x^2-8x+4=\left(3x^2-6x\right)-\left(2x-4\right)=3x\left(x-2\right)-2\left(x-2\right)=\left(x-2\right)\left(3x-2\right)\)

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

b: =3x(x-y)-(x-y)=(x-y)(3x-1)

a,3x²-6xy+3y²

= 3(x²- 2xy+ y²)

= 3(x- y)²

b,xy-9x+y-9

= (xy+ y)- (9x+ 9)

= y(x+ 1)- 9(x+ 1)

= (x+1)(y- 9)

Chúc bạn học tốt

a,\(3x^2-6xy+3y^2\)

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

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

b,xy-9x+y-9

=\(\left(xy+y\right)-\left(9x+9\right)\)

=\(y\left(x+1\right)-9\left(x+1\right)\)

=\(\left(x+1\right)\left(y-9\right)\)

a) Ta có: \(3x^2-6xy+3y^2\)

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

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

b) Ta có: \(xy-9x+y-9\)

\(=x\left(y-9\right)+\left(y-9\right)\)

\(=\left(y-9\right)\left(x+1\right)\)

\(3x^4y-12x^2y^3=3x^2y\left(x^2-4y^2\right)=3x^2y\left(x-2y\right)\left(x+2y\right)\)

\(x^2-y^2-8y-16=x^2-\left(y^2+8y+16\right)=x^2-\left(y+4\right)^2=\left(x+y+4\right)\left(x-y-4\right)\)

\(x^3+3x^2+4x+12=x^2\left(x+3\right)+4\left(x+3\right)=\left(x^2+4\right)\left(x+3\right)\)

\(3x^2-6xy+3y^2-27=3\left[\left(x-y\right)^2-9\right]=3\left(x-y-3\right)\left(x-y+3\right)\)