Question

Пропустила тему сумма и разность кубов. непонимаю как решать уравнения и сокращать. объясните пожалуйста

Answer 1

Сумма кубов : a³+b³=(a+b)(a²-ab+b²)
Вот доказательство тому, что формула a³+b³:
(a+b)(a²-ab+b²)= a³ - a²b + ab² + ba² - ab² + b³ = a³ + b³
Пример: x³ + 27=(x+3)(x²-3x+9)

Разность кубов: a³-b³=(a-b)(a²+ab+b²)
Вот доказательство тому, что формула  a³-b³:
(a-b)(a²+ab+b²)= a³ + a²b + ab² - ba² - ab² - b³ = a³- b³
Пример: x³-8=(x-2)(x²+2x+4)

Answer 2

Understanding the Sum and Difference of Cubes

When dealing with the sum and difference of cubes, it's important to understand the formulas and how to solve equations involving them. Let's break it down step by step.

Sum of Cubes

The sum of cubes formula is given by: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Difference of Cubes

The difference of cubes formula is given by: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Solving Equations and Simplifying

When solving equations involving the sum or difference of cubes, you can use the formulas mentioned above to factorize the expressions. Here's a general approach:

1. Identify if the given expression is a sum of cubes or a difference of cubes. 2. Apply the corresponding formula to factorize the expression. 3. Once factorized, you can simplify the expression further if possible.

For example, if you have an equation like x^3 + 8 = 0, you can recognize it as a sum of cubes where a = x and b = 2. Using the sum of cubes formula, you can factorize it as (x + 2)(x^2 - 2x + 4) = 0.

Conclusion

Understanding the sum and difference of cubes and how to solve equations involving them is essential in algebra. By applying the formulas and simplifying the expressions, you can effectively work through problems related to these concepts. If you have specific equations you'd like to discuss or need further clarification, feel free to provide them for a more detailed explanation.