Question

(a+b)×(a+b)×(a+b)×(a+b)=​

Answer 1

Ответ:

(a + b)^4

Пошаговое объяснение:

(a + b) * (a + b) * (a + b) * (a + b) = (a + b)^4

Answer 2

Ответ:

=ab^4(ab в четвертой степени

Answer 3

To simplify the expression (a+b)×(a+b)×(a+b)×(a+b), we can use the distributive property of multiplication over addition multiple times.

Let's break it down step by step:

Step 1: Start with (a+b)×(a+b): (a+b)×(a+b) = a×(a+b) + b×(a+b) = a×a + a×b + b×a + b×b

Step 2: Expand the expression further: = a² + ab + ba + b²

Step 3: Simplify the expression: Since multiplication is commutative, ba is the same as ab. = a² + ab + ab + b²

Step 4: Combine like terms: = a² + 2ab + b²

Step 5: Now, let's multiply this result by (a+b) again: (a+b)×(a² + 2ab + b²) = a×(a² + 2ab + b²) + b×(a² + 2ab + b²) = a³ + 2a²b + ab² + a²b + 2ab² + b³

Step 6: Simplify further: = a³ + 3a²b + 3ab² + b³

Step 7: Finally, multiply the result by (a+b) one more time: (a+b)×(a³ + 3a²b + 3ab² + b³) = a×(a³ + 3a²b + 3ab² + b³) + b×(a³ + 3a²b + 3ab² + b³) = a⁴ + 3a³b + 3a²b² + ab³ + a³b + 3a²b² + 3ab³ + b⁴

Step 8: Simplify the expression: = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

So, (a+b)×(a+b)×(a+b)×(a+b) simplifies to a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴.