Упростите выражение 35.3-35.4
Ответы
Ответ:
№ 53.3
1) 1000 + a⁶ - (a² + 10)(a⁴ - 10a² + 100) = 1000 + a⁶ - (a⁶ + 1000) =
= 1000 + a⁶ - a⁶ - 1000 = 0
2) (a³ - 9)(a⁶ + 9a³ + 81) - a⁹ - 729 = (a³)³ - 9³ - a⁹ - 729 =
= a⁹ - 729 - a⁹ - 729 = - 1458
3) 0,512t³ - 100 + (0,8t + 5)(0,64t² - 4t + 25) =
= 0,512t³ - 100 + (0,8t)³ + 5³ = 0,512t³ - 100 + 0,512t³ + 125 =
= 1,024t³ + 25
4) (1,1d - c³)(1,21d² + 1,1c³d + c⁶) - 1,331d³ + 2c⁹=
= (1,1d)³ - (c³)³ - 1,331d³ + 2c⁹ =
= 1,331d³ - c⁹ - 1,331d⁹ + 2c⁹ = c⁹
№ 35.4
1) (2 + a⁴)(a⁸ - 2a⁴ + 4) + a¹⁰(1 - a²) = 8 + a¹² + a¹⁰ - a¹² = 8 + a¹⁰
2) k⁵(k + 1) - (3 + k²)(k⁴ - 3k² + 9) = k⁶ + k⁵ - (27 + k⁶) =
= k⁶ + k⁵ - 27 - k⁶ = k⁵ - 27
3) (25 - 5y⁴ + y⁸)(5 + y⁴) - y⁶(y⁶ - 1) = 125 + y¹² - y¹² + y⁶ = 125 + y⁶
4) (z⁶ + 7z³ + 49)(z³ - 7) + z(1 - z⁸) = z⁹ - 343 + z - z⁹ = z - 343