Question

(7х-3у)³+5у(7х-3у)² ​

Answer 1

Для решения данного выражения воспользуемся формулой для возведения разности двух чисел в куб:

(a - b)³ = a³ - 3a²b + 3ab² - b³

Выполним замену переменных: a = 7x, b = 3y. Тогда:

(7x - 3y)³ + 5y(7x - 3y)² = (7x)³ - 3(7x)²(3y) + 3(7x)(3y)² - (3y)³ + 5y[(7x)² - 2(7x)(3y) + (3y)²]

= 343x³ - 567x²y + 315xy² - 27y³ + 5y[49x² - 42xy + 9y²]

= 343x³ - 567x²y + 315xy² - 27y³ + 245x²y - 210xy² + 45y³

= 343x³ - 322x²y + 105xy² + 18y³

Таким образом, выражение (7х-3у)³+5у(7х-3у)² равно 343x³ - 322x²y + 105xy² + 18y³.

Answer 2

To simplify the expression (7x - 3y)³ + 5y(7x - 3y)², we can expand it using the binomial theorem.

Let's start by expanding (7x - 3y)³:

(7x - 3y)³ = (7x - 3y)(7x - 3y)(7x - 3y)

Using the binomial theorem, we can expand this as follows:

(7x - 3y)³ = (7x)³ + 3(7x)²(-3y) + 3(7x)(-3y)² + (-3y)³ = 343x³ - 441x²y + 189xy² - 27y³

Now, let's expand 5y(7x - 3y)²:

5y(7x - 3y)² = 5y(7x - 3y)(7x - 3y)

Using the binomial theorem again, we can expand this as follows:

5y(7x - 3y)² = 5y[(7x)² - 2(7x)(3y) + (-3y)²] = 5y[49x² - 42xy + 9y²] = 245xy² - 210y²x + 45y³

Now, let's add the two expanded expressions together:

(7x - 3y)³ + 5y(7x - 3y)² = 343x³ - 441x²y + 189xy² - 27y³ + 245xy² - 210y²x + 45y³

Combining like terms, we get:

= 343x³ - 441x²y + 434xy² - 27y³ - 210y²x + 45y³

Simplifying further, we have:

= 343x³ - 441x²y - 210y²x + 434xy² + 45y³ - 27y³

= 343x³ - 441x²y - 210y²x + 434xy² + 18y³

So the simplified expression is 343x³ - 441x²y - 210y²x + 434xy² + 18y³.