Question

a power four+a square+1​

Answer 1

Correct Question:

• Factorise a⁴ + a² + 1

Solution:

Given,

= a⁴ + a² + 1

This can be written as,

= a⁴ + 2a² + 1 - a²

= (a⁴ + 2a² + 1) - a²

Now, factorise a⁴ + 2a² + 1,

= a⁴ + a² + a² + 1

= a²(a² + 1) + 1(a² + 1)

= (a² + 1)(a² + 1)

So, the result becomes,

= (a² + 1)² - (a)²

Using identity a² - b² = (a + b)(a - b), we get,

= (a² + a + 1)(a² - a + 1) which is our required answer.

Answer:

• Factorised form - (a² + a + 1)(a² - a + 1).

Answer 2

Step-by-step explanation:

ANSWER ✍️

Correct Question:

Factorise a⁴ + a² + 1

Solution:

Given,

= a⁴ + a² + 1

This can be written as,

= a⁴ + 2a² + 1 - a²

= (a⁴ + 2a² + 1) - a²

Now, factorise a⁴ + 2a² + 1,

= a⁴ + a² + a² + 1

= a²(a² + 1) + 1(a² + 1)

= (a² + 1)(a² + 1)

So, the result becomes,

= (a² + 1)² - (a)²

Using identity a² - b² = (a + b)(a - b), we get,

= (a² + a + 1)(a² - a + 1) which is our required answer.

Answer:

Factorised form - (a² + a + 1)(a² - a + 1).

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