Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.4a^{2} b^{2} -4a^{2} c^{2}\\ b.2c^{2}\\ c.-68x+85\\ d.4\left( a^{2} +b^{2} +c^{2}\right) \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ \left( a^{2} +b^{2} -c^{2}\right)^{2} -\left( a^{2} -b^{2} +c^{2}\right)^{2}\\ =\left( a^{2} +b^{2} -c^{2} -a^{2} +b^{2} -c^{2}\right)\left( a^{2} +b^{2} -c^{2} +a^{2} -b^{2} +c^{2}\right)\\ =\left( 2b^{2} -2c^{2}\right) .2a^{2} =4a^{2} b^{2} -4a^{2} c^{2}\\ b.\ ( a+b+c)^{2} +( a+b-c)^{2} -2( a+b)^{2}\\ =a^{2} +b^{2} +c^{2} +2ab+2bc+2ac+a^{2} +b^{2} +c^{2} +2ab-2ac-2bc-2a^{2} -4ab-2b^{2}\\ =2c^{2}\\ c.\ 4( x+1)^{2} +( 2x-1)^{2} -8( x-1)( x+10)\\ =4x^{2} +8x+4+4x^{2} -4x+1-8\left( x^{2} +9x-10\right)\\ =-68x+85\\ d.\ ( a+b+c)^{2} +( a-b+c)^{2} +( a+b-c)^{2} +( b+c-a)^{2}\\ =a^{2} +b^{2} +c^{2} +2ab+2ac+2bc+a^{2} +b^{2} +c^{2} +2ac-2ab-2bc\\ +a^{2} +b^{2} +c^{2} +2ab-2ac-2bc+a^{2} +b^{2} +c^{2} +2bc-2ac-2ab\\ =4\left( a^{2} +b^{2} +c^{2}\right) \end{array}$

Đáp án+Giải thích các bước giải:

`a)(a^2+b^2-c^2)^2-(a^2-b^2+c^2)^2`

`=a^4+b^4+c^4+2a^2 b^2-2b^2 c^2-2c^2 a^2-a^4-b^4-c^4+2a^2 b^2+2b^2 c^2-2c^2 a^2`

`=4a^2 b^2-4c^2 a^2`

`b)(a+b+c)^2+(a+b-c)^2-2(a+b)^2`

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

`=2a^2+2b^2+2c^2+4ab-2a^2-4ab-2b^2`

`=2c^2`

`c)4(x+1)^2+(2x-1)^2-8(x-1)(x+10)`

`=4(x^2+2x+1)+(4x^2-4x+1)-8(x^2+10x-x-10)`

`=4x^2+8x+4+4x^2-4x+1-8x^2-72x+80`

`=-68x+85`

`d)(a+b+c)^2+(a-b+c)^2+(a+b-c)^2+(b+c-a)^2`

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

`=4a^2+4b^2+4c^2`