Dùng 7 hđt ạ trả lời các câu có dấu tích

Đáp án + Giải thích các bước giải:

Bài `2:`

`a)`

`(x-2)(x^2+2x+4)(x+2)(x^2-2x+4)=0`

`(x^3-8)(x^3+8)=0`

`x^3-8=0` hoặc `x^3+8=0`

`x^3=8` hoặc `x^2=-8`

`x=2` hoặc `x=-2`

Vậy: `x=2` và `x=-2`

`b)`

`(x+4)(x^2-4x+16)-x(x+5)(x-5)=264`

`(x^3+64)-x(x^2-25)=264`

`x^3+64-x^3+25x=264`

`25x+64=264`

`25x=200`

`x=8`

Vậy: `x=8`

`c)`

`(x-2)^3-(x-2)(x^2+2x+4)=6(x+2)(2-x)`

`(x^3-6x^2+12x-8)-(x^3-8)-6(4-x^2)=0`

`x^3-6x^2+12x-8-x^3+8-24+6x^2=0`

`12x-24=0`

`12x=24`

`x=2`

Vậy: `x=2`

Bài `3:`

`a)` `(x^2-2x+4)(x+2)-(x-2)^3-6(x-1)(x+1)`

`=` `(x^3+8)-(x^3-6x^2+12x-8)-6(x^2-1)`

`=` `x^3+8-x^3+6x^2-12x+8-6x^2-1`

`=` `15-12x`

`b)` `(5x-1)^2+2(1-5x)(4+5x)+(5x+4)^2`

`=` `(25x^2-10x+1)+2(4-15x-25x^2)+(25x^2+40x+16)`

`=` `25x^2-10x+1+8-30x-50x^2+25x^2+40x+16`

`=` `25`

`c)` `(x-y)^3+(x+y)^3+(y-x)^3-3xy(x+y)`

`=` `(x+y)^3-3xy(x+y)+(x-y)^3-(x-y)^3`

`=` `(x^3+3x^2y+3xy^2+y^3)-(3x^2y+3xy^2)+0`

`=` `x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2`

`=` `x^3+y^3`

`d)` `3^2*11(10^2+1)(10^4+1)(10^8+1)(10^(16)+1)`

`=` `9*11(10^2+1)(10^4+1)(10^8+1)(10^(16)+1)`

`=` `(10-1)(10+1)(10^2+1)(10^4+1)(10^8+1)(10^(16)+1)`

`=` `(10^2-1)(10^2+1)(10^4+1)(10^8+1)(10^(16)+1)`

`=` `(10^4-1)(10^4+1)(10^8+1)(10^(16)+1)`

`=` `(10^8-1)(10^8-1)(10^(16)+1)`

`=` `(10^(16)-1)(10^(16)+1)`

`=` `10^(32)-1`

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