Question

Factorise : x⁴+x²y²+y⁴ ​

Answer 1

Answer:

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)

Hope it helps you my dear friend..

Step-by-step explanation:

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Answer 2

Hello

To factorise - x^4+x^2y^2+y^4


x^4+x^2y^2+y^4
(x^2)^2 +x^2y^2+(y^2)^2


We know that (a+b)^2 = a^2 + b^2 + 2(a)(b)

= (a+b)^2 - ab = a^2 + b^2 + ab

Here a= x^2 and b= y^2

So we conclude by

(x^2 + y^2)^2 - x^2y^2