Question

factorise: x²+x²y²+y⁴​

Answer 1

This can be factored by completing the square.

Recall that perfect square trinomial x²+2xy+y² = (x+y)².

→ x⁴ + x²y² +y⁴

First term and 3rd term are perfect squares→

→ (x²)² + x²y² + (y²)²

The middle term should to be 2x²y² to make it a perfect square, so add x²y² - x²y²

→ (x²)² + x²y² + (y²)² + x²y² - x²y²

combine 2nd and 4th terms→

→ (x²)² + 2 x²y² + (y²)² - x²y²

First 3 terms form a perfect square trinomial→

→ (x² + y²)²- (xy)²

it is a difference of two squares,

now factor

→ (x² + y² + xy)(x² + y² -xy)

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