Question

A²(a-2)-a(a-3)² представьте в виде произведения

Answer 1

A²(a-2)-a(a-3)²
а*(а²-2а-а²+6а-9)
а*(4а-9)

Answer 2

А2(а-2)-а(а-3)2
а•(а•(-а-2)-(а-3)2
а•(а2-2а-(а2-6а+9))
а•(а2-2а-а2+6а-9)
а•(4а-9)

Answer 3

Simplifying the Expression

To simplify the expression A²(a-2)-a(a-3)² and represent it as a product, we can follow these steps:

1. Expand the squared terms using the formula (a-b)² = a² - 2ab + b². 2. Simplify the resulting expression by combining like terms.

Let's apply these steps to the given expression:

A²(a-2)-a(a-3)²

Expanding the squared terms:

A²(a-2) - a(a² - 2a + 3²)

Simplifying the expression:

A²(a) - A²(2) - a³ + 2a² - 3a²

Combining like terms:

A³ - 2A² - a³ - a²

Now, let's represent this expression as a product.

Representing the Expression as a Product

To represent the expression A³ - 2A² - a³ - a² as a product, we can factor out the common terms.

Factoring out the common terms:

A³ - a³ - 2A² - a²

We can factor out A³ - a³ as (A - a)(A² + Aa + a²).

The expression can be represented as:

(A - a)(A² + Aa + a²) - 2A² - a²

Therefore, the expression A³ - 2A² - a³ - a² can be represented as the product (A - a)(A² + Aa + a²) - 2A² - a².

Please let me know if you need any further assistance.