Question

solve it fast plz
i will mark brainlist​

Answer 1

Required Answer:-

Given to factorise:

• p⁴ + q⁴ + p²q²

Solution:

We have,

p⁴ + q⁴ + p²q²

= p⁴ + q⁴ + [2p²q² - p²q²] [Note that p²q² can be written as 2p²q² - p²q²]

= [ (p²)² + (q²)² + 2 × p² × q²] - p²q²

As you can see that, p⁴ + q⁴ + 2p²q² can be written in a² + 2ab + b² form, factorise it.

= (p² + q²)² - (pq)² [ a² + 2ab + b² = (a + b)²]

We know that a² - b² = (a + b)(a - b), factorise it.

= (p² + pq + q²)(p² - pq + q²)

★ Hence, the factorised form of the polynomial is (p² + pq + q²)(p² - pq + q²)

Answer:

• Factorised form - (p² + pq + q²)(p² - pq + q²)

Answer 2

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Solution:

We have,

p⁴ + q⁴ + p²q²

= p⁴ + q⁴ + [2p²q² - p²q²] [Note that p²q² can be written as 2p²q² - p²q²]

= [ (p²)² + (q²)² + 2 × p² × q²] - p²q²

As you can see that, p⁴ + q⁴ + 2p²q² can be written in a² + 2ab + b² form, factorise it.

= (p² + q²)² - (pq)² [ a² + 2ab + b² = (a + b)²]

We know that a² - b² = (a + b)(a - b), factorise it.

= (p² + pq + q²)(p² - pq + q²)

✒ Hence, the factorised form of the polynomial is (p² + pq + q²)(p² - pq + q²)