Giải bài 1 trang 16

Đề bài

Phân tích các đa thức sau thành nhân tử:

a) $3x^2+6xy$;                  

b) $5\left(y-3\right)-x\left(3-y\right)$;            

c) $2x^3-6x^2$;

d) $x^4{y}^2+x{y}^3$;               

e) $xy-2xyz+x^{2}y$;         

g) ${\left(x+y\right)}^3-x{\left(x+y\right)}^2$.

Lời giải chi tiết

a) $3x^2+6xy=3x.x+2.3xy=3x\left(x+2y\right)$;                       

b) $5\left(y-3\right)-x\left(3-y\right)=5\left(y-3\right)+x\left(y-3\right)=\left(x+5\right)\left(y-3\right)$;            

c) $2x^3-6x^2=2x^2.x-3.2x^2=2x^2\left(x-3\right)$;

d) $x^4{y}^2+x{y}^3=x.x^3{y}^2+x{y}^2.y=x{y}^2\left(x^3+y\right)$;          

e) $xy-2xyz+x^{2}y=xy-2xyz+x.xy=xy\left(1-2z+x\right)$;              

g) ${\left(x+y\right)}^3-x{\left(x+y\right)}^2={\left(x+y\right)}^2\left(x+y\right)-x{\left(x+y\right)}^2={\left(x+y\right)}^2\left(x+y-x\right)=y{\left(x+y\right)}^2$.