Question

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

Answer 1

x^4+2x^2 y^2+ y^4

= x^4 + x^2 y^2+ x^2 y^2 +4y^2

( taking common )

= x^2( x^2+ y^2) + y^2( x^2+ y^2)

=( x^2+ y^2 ) ( x^2+ y^2)

Hope, it helped

Answer 2

Hi there!

Given poly. x⁴ - 2x²y² + y²

Rewrite x⁴ as (x²)² :

(x²)² - 2x²y² + y⁴

Rewrite y⁴ as (y²)² :

(x²)² - 2x²y² + (y²)²

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab = 2 × x² × (−y²)

Simplify.

2ab = −2x²y²

Factor using the perfect square trinomial rule a²−2ab+b² = (a−b)², where a = x² and b = −y²

(x² - y²)²

[ (x + y) (x - y) ] ---[ Factorised. ]

[ Thank you! for asking the question. ]
Hope it helps!