Câu hỏi của Tuyết Ly

Question

Phân tích đa thức thành nhân tử:
a) (x+2)² + 2(x²-4) + (x-2)²
b) x² - x + ¼
c) (x+y)³ - (x-y)³

2611 · Accepted Answer

`a)(x+2)^2+2(x^2-4)+(x-2)^2`

`=(x+2)^2+2(x-2)(x+2)+(x-2)^2`

`=(x+2+x-2)^2=(2x)^2=4x^2`

`b)x^2-x+1/4`

`=x^2-2.x .1/2+1/4=(x-1/2)^2`

`c)(x+y)^3-(x-y)^3`

`=(x+y-x+y)[(x+y)^2+(x+y)(x-y)+(x-y)^2]`

`=2y(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)`

`=2y(3x^2+y^2)`

Câu trả lời:

`a)(x+2)^2+2(x^2-4)+(x-2)^2`

`=(x+2)^2+2(x-2)(x+2)+(x-2)^2`

`=(x+2+x-2)^2=(2x)^2=4x^2`

`b)x^2-x+1/4`

`=x^2-2.x .1/2+1/4=(x-1/2)^2`

`c)(x+y)^3-(x-y)^3`

`=(x+y-x+y)[(x+y)^2+(x+y)(x-y)+(x-y)^2]`

`=2y(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)`

`=2y(3x^2+y^2)`

Trần Tuấn Hoàng · Answer

a) $\left(x+2\right)^2+2\left(x^2-4\right)+\left(x-2\right)^2$

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

$=\left(x+2+x-2\right)^2=\left(2x\right)^2=4x^2$

b) $x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2$

c) $\left(x+y\right)^3-\left(x-y\right)^3=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x^3-3x^2y+3xy^2-y^3\right)=6x^2y+2y^3=2y\left(3x^2+y^2\right)$

Câu trả lời:

a) $\left(x+2\right)^2+2\left(x^2-4\right)+\left(x-2\right)^2$

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

$=\left(x+2+x-2\right)^2=\left(2x\right)^2=4x^2$

b) $x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2$

c) $\left(x+y\right)^3-\left(x-y\right)^3=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x^3-3x^2y+3xy^2-y^3\right)=6x^2y+2y^3=2y\left(3x^2+y^2\right)$

Hào Nguyễn quang · Answer

$a)(x+2)2+2(x2-4)+(x-2)2a)(x+2)2+2(x2-4)+(x-2)2$

$=(x+2)2+2(x-2)(x+2)+(x-2)2$

$=(x+2+x-2)2=(2x)2=4x2$

$b)x2-x+14b)x2-x+14$

$=x2-2.x.12+14$

$=(x-12)2=x2-2.x.12+14$

$=(x-12)2$

$c)(x+y)3-(x-y)3c)(x+y)3-(x-y)3$

$=(x+y-x+y)[(x+y)2+(x+y)(x-y)+(x-y)2]$

$=2y(x2+2xy+y2+x2-y2+x2-2xy+y2)$

$=2y(3x2+y2)$

Câu trả lời:

$a)(x+2)2+2(x2-4)+(x-2)2a)(x+2)2+2(x2-4)+(x-2)2$

$=(x+2)2+2(x-2)(x+2)+(x-2)2$

$=(x+2+x-2)2=(2x)2=4x2$

$b)x2-x+14b)x2-x+14$

$=x2-2.x.12+14$

$=(x-12)2=x2-2.x.12+14$

$=(x-12)2$

$c)(x+y)3-(x-y)3c)(x+y)3-(x-y)3$

$=(x+y-x+y)[(x+y)2+(x+y)(x-y)+(x-y)2]$

$=2y(x2+2xy+y2+x2-y2+x2-2xy+y2)$

$=2y(3x2+y2)$

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