Răspuns:
Explicație pas cu pas:
( a + b)⁴ = a⁴ + 4 a³b + 6 a²b² + 4a³b + b⁴
= ( a + b)²(a+b)² =
= (a²+2ab+b²)(a²+2ab+b²) =
= a⁴ + 2 a³b + a²b² + 2 a³b + 4a²b² + 2ab³ + a²b² + 2ab³+b⁴ =
= a⁴ + 4 a³b + 6 a²b² + 4a³b + b⁴
SAU:
= ( a+b)(a+b)³ = (a+b)(a³ + 3a²b + 3ab²+b³) =
= a⁴ + a³b + 3a³b + 3 a²b² + 3a²b² + 3ab³+ab³+ b⁴ =
= a⁴ + 4 a³b + 6 a²b² + 4 ab³+ b⁴
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( a-b)⁴ = a⁴ - 4a³b + 6a²b² - 4ab³ + b⁴ ( formula)
= (a-b)²(a-b)² =
= ( a² - 2ab + b²)(a²- 2ab + b²) =
= a⁴- 2a³b + a²b² - 2a³b + 4a²b² - 2ab³ + a²b² - 2ab³ + b⁴ =
= a⁴ - 4a³b + 6a²b² - 4ab³ + b⁴
