`a)`

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

`= 2x(4x^2 - 4x + 1) - 3x(x^2 - 9) - 4x(x^2 + 2x + 1)`

`= 8x^3 - 8x^2 + 2x - 3x^3 + 27x - 4x^3 - 8x^2 - 4x`

`= x^3 - 16x^2 + 25x `

`b)`

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

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

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

`= a^2`

`c)`

`(3x + 1)^2 - 2(3x + 1)(3x + 5) + (3x + 5)^2`

`= (3x + 1 - 3x - 5)^2 `

`= (-4)^2`

`= 16`

`d)`

`Đặt  A = 4(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)`

`⇒ 2A = 8(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)`

`⇒ 2A = (3^2 - 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)`

`⇒ 2A = (3^4 - 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)`

`⇒ 2A = (3^8 - 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)`

`⇒ 2A = (3^16 - 1)(3^16 + 1)(3^32 + 1)`

`⇒ 2A = (3^32 - 1)(3^32 + 1)`

`⇒ 2A = 3^64 - 1 `

`⇒ A = (3^64 - 1)/2`

Đáp án+Giải thích các bước giải:

 `a)`

`2x(2x-1)^2-3x(x+3)(x-3)-4x.(x+1)^2`

`=2x(4x^2-4x+1)-3x(x^2-9)-4x(x^2+2x+1)`

`=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x`

`=(8x^3-3x^3-4x^3)+(-8x^2-8x^2)+(2x+27x-4x)`

`=x^3-16x^2+25x`

`b)`

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

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

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

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

`=a^2`

`c)`

`(3x+1)^2-2(3x+1)(3x+5)+(3x+5)^2`

`=[(3x+1)-(3x+5)]^2`

`=(3x+1-3x-5)^2`

`=(-4)^2`

`=16`

`d)`

`4(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)`

`=1/(2).8.(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)`

`=1/(2).(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)`

`=1/(2).(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)`

`=1/(2).(3^8-1)(3^8+1)(3^16+1)(3^32+1)`

`=1/(2).(3^16-1)(3^16+1)(3^32+1)`

`=1/(2).(3^32-1)(3^32+1)`

`=1/(2).(3^64-1)`

`=(3^64-1)/2`