Câu 3:
a/ `y^2+2y+1`
`= y^2+2y.1+1^2`
`=(y+1)^2`
b/ `9x^2+y^2-6xy`
`= (3x)^2-2.3xy+y^2`
`=(3x-y)^2`
c/ `25a^2+4b^2+20ab`
`= (5a)^a+2.5a.2b+(2b)^2`
`= (5a+2b)^2`
d/ `x^2-x+1/4`
`= x^2-2.x.1/2+(1/2)^2`
`=(x-1/2)^2`
Câu 4:
a/ `14x^2y-21xy^2+28x^y^2`
`= 7xy.2x-7xy.3y+7xy.4xy`
`= 7xy(2x-3y+4xy)`
b/ `27x^3-1/27`
`= (3x)^3-(1/3)^3`
`= (3x-1/3)(9x^2+x+1/9)`
c/ `3x^2-3xy-5x+5y`
`= (3x^2-3xy)-(5x-5y)`
`= 3x(x-y)-5(x-y)`
`=(x-y)(3x-5)`
d/ `x^2+7x+12`
`= (x^2+3x)+(4x+12)`
`= x(x+3)+4(x+3)`
`=(x+3)(x+4)`
Câu 5:
a/ `x(x-2)+x-2=0`
`⇔ x(x-2)+(x-2)=0`
`⇔ (x-2)(x+1)=0`
⇔ \(\left[ \begin{array}{l}x-2=0\\x+1=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=2\\x=-1\end{array} \right.\)
b/ `5x(x-3)-x+3=0`
`⇔ 5x(x-3)-(x-3)=0`
`⇔ (x-3)(5x-1)=0`
⇔ \(\left[ \begin{array}{l}x-3=0\\5x-1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=3\\x=\frac{1}{5}\end{array} \right.\)
