b: =(x-5)(x+3)

f: \(=\left(2x+3\right)^2\)

\(a,=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ b,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ c,=5x^2y^3\left(1-5xy+2x\right)\\ d,=6y\left(2x^2-3xy-10y\right)\\ e,,=\left(x-y\right)\left(5-x\right)\\ f,=\left(2x+3\right)^2\)

b: Ta có: \(xy-3x-2y+6\)

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

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

1, x^3-2x^2+x

=x^3-x^2-x^2+x

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

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

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

=x(x-1)(x-1)

2, x^2-2x-15

=x^2-2x-9-6

= x^2-9-2x-6

=(x^2-9)-(2x+6)

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

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

3 , \(^{3x^3y^2-6x^2y^3+9x^2y^2}\)

= \(^{3x^2y^2\left(x-2y+3\right)}\)

4,  \(^{5x^2y^3-25x^3y^4+10x^3y^3}\)

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

5, \(^{12x^2y-18xy^2-30y^2}\)

=\(^{3y\left(4x^2-6xy-10y\right)}\)

Lời giải:
1. $x^3-2x^2+x=x(x^2-2x+1)=x(x-1)^2$
2. $x^2-2x-15=(x^2+3x)-(5x+15)=x(x+3)-5(x+3)=(x+3)(x-5)$

3. $3x^3y^2-6x^2y^3+9x^2y^2=3x^2y^2(x-2y+3)$

4. $5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3(1-5xy+2x)$
5. $12x^2y-18xy^2-30y^2=6y(2x^2-3xy-5y)$

Bạn cần viết đề bằng công thức toán để được hỗ trợ tốt hơn.

a) 3x . ( x-1 ) = 3x² - 3x 

b) x³- 2x²+x = x².( x-1 ) - x.( x-1 ) = (x-1).(x-1).x 

= (x-1)².x 

c) x²- 2xy-9z²+y²

= (x²-2xy+y² )-(3z)²

= (x-y)²-(3z)²

= ( x-y-3z).(x-y+3z)

thay vào ta có ( 6+4-90 ).(6+4+90 )=-80.100=-8000 

\(a,=\left(x+1\right)\left(x+3\right)\\ b,=-5x^2+15x+x-3=\left(x-3\right)\left(1-5x\right)\\ c,=2x^2+2x+5x+5=\left(2x+5\right)\left(x+1\right)\\ d,=2x^2-2x+5x-5=\left(x-1\right)\left(2x+5\right)\\ e,=x^3+x^2-4x^2-4x+x+1=\left(x+1\right)\left(x^2-4x+1\right)\\ f,=x^2+x-5x-5=\left(x+1\right)\left(x-5\right)\)

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

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

\(a,=3\left(x^2-2\right)\\ b,=\left(x-1\right)^2-y^2=\left(x-y-1\right)\left(x+y-1\right)\\ c,=9x^2\left(x-y\right)-4\left(x-y\right)=\left(3x-2\right)\left(3x+2\right)\left(x-y\right)\\ d,=x\left(x^2-2x-8\right)=x\left(x^2+2x-4x-8\right)=x\left(x+2\right)\left(x-4\right)\)