Question

9. Розкласти на множники: a) a⁴ + a² + 1; 6) x⁴ + x²y² + y⁴; B) a⁶ + 1.​

Answer 1

Ответ:

Объяснение:

a) a⁴ + a² + 1 = (a²+a+1)(a²-a+1);

6) x⁴ + x²y² + y⁴ = (x²-xy+y²)(x²+xy+y²);

B) a⁶ + 1=(a²)³ +1=(a²+1)(a⁴-a²+1).

Answer 2

I will try to answer your question in detail. Here is how to factorize the following expressions:

a) a⁴ + a² + 1

This expression is a sum of cubes, which can be factorized using the formula:

a³ + b³ = (a + b)(a² - ab + b²)

In this case, we can write:

a⁴ + a² + 1 = (a²)² + (1)² + 2a²

= (a² + 1)² - (2a)²

= (a² + 1 + 2a)(a² + 1 - 2a)

= (a² + 2a + 1)(a² - 2a + 1)

b) x⁴ + x²y² + y⁴

This expression is a perfect square trinomial, which can be factorized using the formula:

a² + 2ab + b² = (a + b)²

In this case, we can write:

x⁴ + x²y² + y⁴ = (x²)² + 2x²y² + (y²)²

= (x² + y²)²

c) a⁶ + 1

This expression is a sum of sixth powers, which can be factorized using the formula:

a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)

In this case, we can write:

a⁶ + 1 = (a² + 1)(a⁴ - a² + 1)