Question

[Đặng Thị Cẩm Tú]

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

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

- Cho thêm 1 VD về dạng: rút gọn biểu thức(y như trên) rồi trình bày chi tiết:

* Lưu ý: Không được trùng với 4 bài trên

Answer 1

[Hoàng Thị Ngọc Anh]

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!

Answer 2

[Hoàng Thị Ngọc Anh]

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

\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+2a^2+2ab+b^2\)

\(=4a^2+4b^2+2c^2+6ab.\)