Question

Упростить выражение: (3x+x^2)^2-x^2(x-5)(x+5)+2x(8-3x^2) 'Где ^ степень' ответ вроде-бы 34x^2+16x, но учитель говорит то, что не верно, срочно нужна помощь, и обязательно полное решение.

Answer 1

Ответ верный... а "что-то неверное" может быть внутри решения)))

Answer 2

Simplifying the Expression

To simplify the expression (3x+x^2)^2-x^2(x-5)(x+5)+2x(8-3x^2), we can follow these steps:

Step 1: Expand the squared term (3x+x^2)^2. Step 2: Simplify the expression x^2(x-5)(x+5). Step 3: Simplify the expression 2x(8-3x^2). Step 4: Combine the simplified terms.

Let's go through each step in detail.

Step 1: Expand the squared term (3x+x^2)^2. To expand this squared term, we can use the formula (a+b)^2 = a^2 + 2ab + b^2.

In our case, a = 3x and b = x^2. So, (3x+x^2)^2 = (3x)^2 + 2(3x)(x^2) + (x^2)^2 = 9x^2 + 6x^3 + x^4.

Step 2: Simplify the expression x^2(x-5)(x+5). To simplify this expression, we can use the distributive property.

Expanding the expression, we get: x^2(x-5)(x+5) = x^2(x^2 - 5x + 5x - 25) = x^2(x^2 - 25) = x^4 - 25x^2.

Step 3: Simplify the expression 2x(8-3x^2). To simplify this expression, we can use the distributive property.

Expanding the expression, we get: 2x(8-3x^2) = 2x(8) - 2x(3x^2) = 16x - 6x^3.

Step 4: Combine the simplified terms. Now, we can combine the simplified terms from Steps 1, 2, and 3.

The simplified expression is: (9x^2 + 6x^3 + x^4) - (x^4 - 25x^2) + (16x - 6x^3) = 9x^2 + 6x^3 + x^4 - x^4 + 25x^2 + 16x - 6x^3.

Simplifying further, we can combine like terms: 9x^2 + 25x^2 + 6x^3 - 6x^3 + 16x = 34x^2 + 16x.

Therefore, the simplified expression is 34x^2 + 16x.

Please note that this is the simplified form of the expression based on the given input. If your teacher is saying it is incorrect, there might be a misunderstanding or a mistake in the input or the expected answer. It would be best to clarify with your teacher to ensure you have the correct information.

Let me know if you need any further assistance!