1. Домножим и разделим первое слагаемое на 2²-1, получим
1
* ( (2²-1)(2²+1)*(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1) ) -1/3 *2¹²⁸ =
2²-1
=1/3*( (2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1) )- 1/3*2¹²⁸=
=1/3*( (2⁸-1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1) )-1/3*2¹²⁸ =
=1/3*( (2¹⁶-1)(2¹⁶+1)(2²+1)(2⁶⁴+1) )-1/3*2²⁸ =
=1/3*( (2³²-1)(2³²+1)(2⁶⁴+1) ) -1/3*2²⁸= 1/3( (2⁶⁴-1)(2⁶⁴+1) )-1/3*2¹²⁸ =
=1/3*( 2¹²⁸-1)-1/3*2¹²⁸= 1/3*2¹²⁸ - 1/3 - 1/3*2¹²⁸ = -1/3
2) (8ab+5)(5-8ab)=5²-(8ab)²=25-64a²b²
3) (8+9cd)(9cd-8)=(9cd)²-8²=81c²d²-64
1) (a²+b²)(a²-b²)= (a²)² - (b²)²=a^4 - b^4
2) (10m²-n²)(10m²+n²)=100m^4-n^4
3) (5-x)(5+x)(25+x²)= (25-x²)(25+x²)= 625-x^4