Question

(x-y)(x+y)(x⁴+x²y²+y⁴)​

Answer 1

Ответ:

x^6-y^6

Объяснение:

(x-y)(x+y)(x^4+x^2y^2+y^4)=(x^2-y^2)(x^4+x^2y^2+y^4)=x^6-y^6.

^ - это степень если что

Answer 2

The expression you've given is a polynomial expression that can be simplified by using the difference of squares and factoring techniques. Let's break it down step by step:

1. Start with the given expression: (x - y)(x + y)(x⁴ + x²y² + y⁴)

2. Use the difference of squares identity (a² - b²) = (a + b)(a - b) to factor the first two terms: (x - y)(x + y)

Now, the expression looks like this: (x - y)(x + y)(x⁴ + x²y² + y⁴)

3. Notice that the remaining part of the expression x⁴ + x²y² + y⁴ is the sum of cubes, which can be factored using the sum of cubes identity (a³ + b³) = (a + b)(a² - ab + b²). In this case, a = x² and b = y²: x⁴ + x²y² + y⁴ = (x²)³ + (y²)³

Now, apply the sum of cubes identity: (x²)³ + (y²)³ = (x² + y²)(x⁴ - x²y² + y⁴)

So, your expression is now factored as: (x - y)(x + y)(x² + y²)(x⁴ - x²y² + y⁴)

That's the fully factored form of the given expression.