Question

factorise the following x⁴+x²y²+y⁴​

Answer 1

Step-by-step explanation:

Given :-

x⁴+x²y²+y⁴

To find :-

Factorise the expression x⁴+x²y²+y⁴ ?

Solution :-

Given expression is x⁴+x²y²+y⁴

On adding and subtracting x²y²

=> x⁴+x²y²+y⁴+x²y²-x²y²

=> x⁴+2x²y²+y⁴-x²y²

=> (x⁴+2x²y²+y⁴)-(x²y²)

It can be written as

=> [(x²)²+2(x²)(y²)+(y²)²] -(x²y²)

=> (x²+y²)²-(x²y²)

Since (a+b)² = a²+2ab+b²

Where , a = x² and b = y²

=> (x²+y²)²-(xy)²

It is in the form of a²-b²

Where a = x²+y² and b = xy

We know that

(a+b)(a-b) = a²-b²

=> (x²+y²+xy)(x²+y²-xy)

=> (x²+xy+y²)(x²-xy+y²)

Therefore,

x⁴+x²y²+y⁴ = (x²+xy+y²)(x²-xy+y²)

Answer:-

The factorization of x⁴+x²y²+y⁴ is

(x²+xy+y²)(x²-xy+y²)

Used formulae:-

• (a+b)² = a²+2ab+b²

• (a+b)(a-b) = a²-b²