factorise: x²+x²y²+y⁴
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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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