x⁴+ 9x²y²
+ 81y4 factorise
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Step-by-step explanation:
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 trionomial
= (x² + y²)²- (xy)² it is a difference of two squares, now factor
=(x² + y² + xy)(x² + y² - xy)
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