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

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

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

5: \(y^2\left(x^2+y\right)-z\cdot x^2-zy\)

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

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

7: \(5\left(x+y\right)^2+15\left(x+y\right)\)

\(=5\left(x+y\right)\cdot\left(x+y\right)+5\left(x+y\right)\cdot3\)

=5(x+y)(x+y+3)

9: \(7x\left(y-4\right)^2-\left(4-y\right)^3\)

\(=7x\left(y-4\right)^2+\left(y-4\right)^3\)

\(=\left(y-4\right)^2\left(7x+y-4\right)\)

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

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

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

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

2: \(5x\left(x-2\right)-3x^2\left(x-2\right)\)

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

4: 3x(x-5y)-2y(5y-x)

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

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

6: b(a-c)+5c-5a

=b(a-c)-5(a-c)

=(a-c)(b-5)

8: 9x(x-y)-10(y-x)^2

=9x(x-y)-10(x-y)^2

=(x-y)(9x-10x+10y)

=(x-y)(-x+10y)

10: \(\left(a-b\right)^2-\left(a+b\right)\left(b-a\right)\)

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

=(a-b)(a-b+a+b)

=2a(a-b)

12: 2x(x-3)+y(x-3)+(3-x)

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

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

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

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

2) \(4x(x-2y)-8y(2y-x)\)

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

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

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

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

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

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

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

4) \(3x\left(x-a\right)+4a\left(a-x\right)\)

\(=3x\left(x-a\right)-4a\left(x-a\right)\)

\(=\left(x-a\right)\left(3x-4a\right)\)

5) \(5x\left(x-y\right)^2+10y^2\left(y-x\right)^2\)

\(=5x\left(x-y\right)^2+10y^2\left(x-y\right)^2\)

\(=\left(5x+10y^2\right)\left(x-y\right)^2\)

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

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

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

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

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

7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)

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

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

8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)

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

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

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

#Ayumu

1) \(5x-5y+x\left(x-y\right)\)

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

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

2) \(x^2+4x+3\)

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

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

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

3) \(x^2-2xy+y^2-z^2\)

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

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

4) \(x\left(x-5\right)-3x+15\)

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

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

5) \(y^2-x^2+2x-1\)

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

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

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

\(1.\left(x-y\right)\left(x+5\right)\)

\(2.\left(x+1\right)\left(x+3\right)\)

\(3.\left(x-y-z\right)\left(x-y+z\right)\)

\(4.\left(x-3\right)\left(x-5\right)\)

\(5.\left(y-x+1\right)\left(y+x+1\right)\)

\(7.\left(x+1\right)\left(x-2\right)^2\)

\(8.\left(x-5\right)\left(x+3\right)\)

\(10.\left(y+1\right)\left(2x+z\right)\)

1)

5x - 5y + x ( x - y ) = (x-y)(5+x)

2)

x²+4x+3=x²+x+3x+3=(x+1)(x+3)

3)x²-2xy+y²-z²=\(\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

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