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

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

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

= \(12x-4\)

2,105 km = 2105 m

A = \(2x^2-11x+9\)

A = \(2x^2-2x-9x+9\)

A = \(2x\left(x-1\right)-9\left(x-1\right)=\left(x-1\right)\left(2x-9\right)\)

B = \(3x^4-4x^3+2x^2-5x+4\)

B = \(3x^4-3x^3-x^3+x^2+x^2-x-4x+4\)

B=\(3x^3\left(x-1\right)-x^2\left(x-1\right)+x\left(x-1\right)-4\left(x-1\right)\)

B = \(\left(x-1\right)\left(3x^3-x^2+x-4\right)\)

C = \(x^3-x^2+4x-12\)

C = \(x^3-2x^2+x^2-2x+6x-12\)

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

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

B1:

a) \(3^{n+1}+3^{n+2}=324\)

\(3^n.3+3^n.3^2=324\)

\(3^n.12=324\)

\(3^n=27\)

\(3^n=3^3\Rightarrow n=3\)

b) \(4^{n-1}-4^n=192\)

-1 = 192 ( vô lí )

Vậy k có n thoả mãn -_-

B1:

A = \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)

A = \(4x^2+4x+1+8x^2-2+4x^2-4x+1\)

A = \(16x^2\)

B = \(x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)

B = \(x\left(x^2-16\right)-x^4+1\)

B = \(x^3-16x-x^4+1\)

C = \(\left(x^2-1\right)\left(x-3\right)-\left(x-3\right)\left(x^2+3x+9\right)\)

C = \(x^3-3x^2-x+3-x^3+27\)

C = \(-3x^2-x+30\)

\(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

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

Đặt \(x^2+3x=a\)

Pt (*) \(\Leftrightarrow a.\left(a+2\right)+1\) = \(a^2+2a+1\) = \(\left(a+1\right)^2\)

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