Câu hỏi của Đặng Thị Cẩm Tú

Question

Rút gọn biểu thức:

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

b/ $\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)$

c/ \(\left(a...

Hoàng Thị Ngọc Anh · Accepted Answer

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

$=\left(x^3-2x^2-2x^2+4x+2x-4\right)\left(x^3+2^3\right)$

$=\left(x^3-4x^2+6x-4\right)\left(x^3+8\right)$

$=x^6+8x^3-4x^5-32x^2+6x^4+48x-4x^3-32$

$=x^6-4x^5+4x^3-32x^2+48x-32$

b) $\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)$

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

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

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

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

$=2x^3+6x-2x^3+3x$

$=9x$

2 câu kia đợi tí đã nhé!Câu trả lời: a) $\left(x^2-2x+2\right)\left(x-2\right)\left(x^2-2x+2\right)\left(x+2\right)$

$=\left(x^3-2x^2-2x^2+4x+2x-4\right)\left(x^3+2^3\right)$

$=\left(x^3-4x^2+6x-4\right)\left(x^3+8\right)$

$=x^6+8x^3-4x^5-32x^2+6x^4+48x-4x^3-32$

$=x^6-4x^5+4x^3-32x^2+48x-32$

b) $\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)$

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

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

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

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

$=2x^3+6x-2x^3+3x$

$=9x$

2 câu kia đợi tí đã nhé!

Hoàng Thị Ngọc Anh · Answer

c) $\left(a+b+c\right)^2+\left(a+b-c\right)^2+\left(2a-b\right)^2$

$=\left(a^2+b^2+c^2+2ab+2bc+2ca\right)+\left(a^2+b^2+c^2+2ab-2bc-2ca\right)+\left(4a^2-4ab+b^2\right)$

$=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+4a^2-4ab+b^2$

$=6a^2+3b^2+2c^2$

d) $\left(a+b+c\right)^2+\left(a+b-c\right)^2+2\left(a+b\right)^2$

$=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+2a^2+2ab+b^2$

$=4a^2+4b^2+2c^2+6ab.$Câu trả lời: c) $\left(a+b+c\right)^2+\left(a+b-c\right)^2+\left(2a-b\right)^2$

$=\left(a^2+b^2+c^2+2ab+2bc+2ca\right)+\left(a^2+b^2+c^2+2ab-2bc-2ca\right)+\left(4a^2-4ab+b^2\right)$

$=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+4a^2-4ab+b^2$

$=6a^2+3b^2+2c^2$

d) $\left(a+b+c\right)^2+\left(a+b-c\right)^2+2\left(a+b\right)^2$

$=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+2a^2+2ab+b^2$

$=4a^2+4b^2+2c^2+6ab.$

Nguyễn Thị Huyền Trang · Answer

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

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

$=\left(x^2+4x^2+4-4x^3+4x^2-8x\right)\left(x^2-4\right)$

$=\left(-4x^3+9x^2-8x+4\right)\left(x^2-4\right)$

$=-4x^5+16x^3+9x^4-36x^2-8x^3+32x+4x^2-16$

$=-4x^5+9x^4+8x^3-32x^2+32x-16$

b, $\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)$

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

$=2x^3+6x-3x^3+3x=-x^3+9x$Câu trả lời: a, $\left(x^2-2x+2\right)\left(x-2\right)\left(x^2-2x+2\right)\left(x+2\right)$