phân tích đa thức thành nhân tử a)x ³+2x ²y+xy ²-4x b)8a ³+4a ²b-2ab ²-b ³ c)x ²-2xy+y ²-3x+3y+2

Đáp án:

a) $= x\left ( x+y+2 \right )\left ( x+y-2 \right )$

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

c) $= \left ( x-y-1 \right )\left ( x-y-2 \right )$

Giải thích các bước :

a)

$x^{3}+2x^{2}y+xy^{2}-4x$
 $= x\left ( x^{2}+2xy+y^{2}-4 \right )$
 $= x\left [ \left ( x+y \right ) ^{2}-4\right ]$
 $= x\left ( x+y+2 \right )\left ( x+y-2 \right )$

b)

$8a^{3}+4a^{2}b-2ab^{2}-b^{3}$
$= \left ( 8a^{3}-b^{3} \right )+\left ( 4 a^{2}b-2ab^{2}\right )$
$= \left ( 2a-b \right )\left ( 4a^{2}+2ab+b^{2} \right )+2ab\left ( 2a-b\right )$
$= \left ( 2a-b \right )\left ( 4a^{2}+2ab+b^{2}+2ab \right )$
$= \left ( 2a-b \right )\left ( 2a+b \right )^{2}$

c)

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