Câu hỏi của Măm Măm

Question

Phân tích đa thức sau thành phân tử;

$g,x^2-2xy+y^2-z^2$

$h,9x^2y^2+6xy^2+y^2-1$

$i,x^2-x-2$

Khôi Bùi · Accepted Answer

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

h ) $9x^2y^2+6xy^2+y^2-1$

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

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

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

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

$=\left(3xy+y-1\right)\left(3xy+y+1\right)$

i ) $x^2-x-2=x^2-x+\dfrac{1}{4}-\dfrac{9}{4}=\left(x-\dfrac{1}{2}\right)^2-\left(\dfrac{3}{2}\right)^2=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)=\left(x-2\right)\left(x+1\right)$Câu trả lời: g ) $x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)$