Question

Bái 1: Rút gọn các biểu thức sau:

1. (a+b+c)²+(a-b-c)²+(b-c-a)²+(c-a-b)²

2. (a+b-c)²+(a-b+c)²-2.(b-c)²

3. (x+1)³-(x-1)³-6.(x-1)²

Answer 1

các bạn ơi giúp mình với

Answer 2

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

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

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

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

= \(a^2+b^2+c^2+2ab-2bc-2ac+a^2+b^2+c^2-2ab+2bc+2ac-2b^2+4bc-2c^2\)

= \(2a^2+4bc\)

3) \(\left(x+1\right)^3-\left(x-1\right)^3-6.\left(x-1\right)^2\)

= \(x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-2x+1\right)\)

= \(6x^2+2-6x^2+12x-6\)

= \(12x-4\)

Answer 3

1.= a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2-2ab+2bc+2ca +a^2+b^2+c^2 -2bc+2ca-2ab+a^2+b^2+c^2-2ca+2ab-2bc

=4(a^2+b^2+c^2)

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

=2(a^2+c^2)

Thấy được thì tick đúng nhé!

Answer 4

\(1.\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\\ =a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+c^2-2ab-2ac+2bc+b^2+c^2+a^2-2ab-2bc+2ac\\ =3a^2+3b^2+3c^2-2ab+2ac+2bc\)\(2.\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\\ =a^2+b^2+c^2+2ab-2ac-2bc+a^2+b^2+c^2-2ab-2bc+2ac-2b^2+4bc-2c^2\\ =a^2\)\(3.\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2\\ =x^3+3x^2+3x+1-x^3-3x^2+3x-1-6x^2+12x-6\\ =-6x^2+18x-6\)

Answer 5

Bài 1:

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

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

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

\(=2\left[\left(a+b\right)^2+\left(a-b\right)^2\right]+4c^2\)

\(=4\left(a^2+b^2+c^2\right)\)

Bài 2:

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

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

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

\(=2a^2\)

Bài 3 cũng tương tự nha bạn.

Chúc bạn học tốt!