Question

Помогите решить и объясните, пожалуйста40c^2-10d^2/20c^2+20cd+5d^2/ - дробная черта

Answer 1

Я так понимаю, нужно сократить? 
в числителе выноси общий множитель за скобки: 40с^2-10d^2 = 10(4c^2-d^2)  тогда выражение в скобках можно разложить по формуле сокращенного умножения (т.к 4=2^2) . Получается 10(2с-d)(2c+d)
В знаменателе также выносим общий множитель: 20c^2+20cd+5d^2=5(4c^2+4cd+d^2)  теперь выражение в скобках можно преобразовать по формулу сокращенного умножения: 5(4c^2+4cd+d^2)=5(2c+d)^2
Далее сокращаются (2с+d)  и 10 , получается выражение 2(2с-d)/2c+d

Answer 2

Solving the Expression

To solve the given expression 40c^2 - 10d^2 / 20c^2 + 20cd + 5d^2, we can follow these steps:

1. Factorize the numerator and denominator separately. 2. Simplify the expression by canceling out common factors. 3. Express the simplified form of the expression.

Let's proceed with the solution.

Step 1: Factorization

First, let's factorize the numerator and denominator separately.

Numerator: 40c^2 - 10d^2 - Factor out the common factor, which is 10: 10(4c^2 - d^2) - Recognize that this is a difference of squares, so it can be further factorized as: 10(2c + d)(2c - d)

Denominator: 20c^2 + 20cd + 5d^2 - Factor out the common factor, which is 5: 5(4c^2 + 4cd + d^2) - Recognize that this is a perfect square trinomial, so it can be further factorized as: 5(2c + d)^2

Now, the expression becomes: (10(2c + d)(2c - d)) / (5(2c + d)^2)

Step 2: Simplification

Next, we can simplify the expression by canceling out common factors. Since both the numerator and denominator have a common factor of 5, we can simplify further.

The simplified form of the expression is: (2(2c - d)) / (2c + d)

Step 3: Final Expression

The final simplified expression is: (2(2c - d)) / (2c + d).

So, the solution to the given expression 40c^2 - 10d^2 / 20c^2 + 20cd + 5d^2 is (2(2c - d)) / (2c + d).

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.