Đáp án:
Giải thích các bước giải:
Bài 1:
a) 20x - 5y
⇒ 5(4x - y)
b) 20x²y - 12x³
⇒ 4x²(5y - 3x)
c) 4x²y - 8xy² + 10x²y²
⇒ 2xy(2x - 4y + 5xy)
d) 14x²y - 21xy² + 28x²y²
⇒ 7xy(2x - 3y + 4xy)
Bài 2:
a) x+6x²=0
⇔x(1+6x)=0
⇔$\left \{ {{x=0} \atop {1+6x=0}} \right.$
⇔$\left \{ {{x=0} \atop {x=\frac{-1}{6}}} \right.$
b) x²-4x=0
⇔x(x-4)=0
⇔$\left \{ {{x=0} \atop {x-4=0}} \right.$
⇔$\left \{ {{x=0} \atop {x=4}} \right.$
c) 4x(x+1)-8(x+1)=0
⇔(4x-8)(x+1)=0
⇔$\left \{ {{4x-8=0} \atop {x+1=0}} \right.$
⇔$\left \{ {{x=2} \atop {x=-1}} \right.$
d) 5x(x-2000)-x+2000 =0
⇔5x(x-2000)-(x-2000)=0
⇔(5x-1)(x-2000)=0
⇔$\left \{ {{5x-1=0} \atop {x-2000=0}} \right.$
⇔$\left \{ {{x=\frac{1}{5}} \atop {x=2000}} \right.$
e) x(x-1)-2(x-1)=0
⇔(x-2)(x-1)=0
⇔$\left \{ {{x-2=0} \atop {x-1=0}} \right.$
⇔$\left \{ {{x=2} \atop {x=1}} \right.$
f) 5x(x-2)-(2-x) =0
⇔5x(x-2)+(x-2) =0
⇔(5x+1)(x-2) =0
⇔$\left \{ {{5x+1=0} \atop {x-2=0}} \right.$
⇔$\left \{ {{x=\frac{-1}{5}} \atop {x=2}} \right.$
g) (1-x)²-1+x=0
⇔(1-x)²-(1-x)=0
⇔(1-x)(1-x-1)=0
⇔-x(1-x)=0
⇔$\left \{ {{x=0} \atop {1-x=0}} \right.$
⇔$\left \{ {{x=0} \atop {x=1}} \right.$
h) (x+1)=(x+1)²
⇔(x+1)-(x+1)²=0
⇔(x+1)(1-x-1)=0
⇔-x(x+1)=0
⇔$\left \{ {{x=0} \atop {x+1=0}} \right.$
⇔$\left \{ {{x=0} \atop {x=-1}} \right.$
