Question

factorise - a4+ a2b2 + b4

Answer 1

We have, a4+ a2b2 + b4

It can be factorized as:

a4+ a2b2 + b4+ a2b2 - a2b2 = a4+ 2a2b2 + b4 - a2b2

= (a2 + b2)2 - (ab)2

= (a2 + b2 + ab)(a2 + b2 - ab)  [Using: x2 - y2 = (x+y)(x-y)] 

Answer 2

Given : The algebraic expression is, a⁴+a²b²+b⁴

To find : The factorisation of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the algebraic expression)

Here, we will be using general algebraic method. (we will be using algebraic identities, whenever needed)

So,

= a⁴ + a²b² + b⁴

= a⁴ + a²b² + b⁴ + a²b² - a²b²

= a⁴ + a²b² + a²b² + b⁴- a²b²

= a⁴ + 2a²b² + b⁴ - a²b²

= [(a²)² + (2 × a² × b²) + (b²)²] - (ab)²

= (a²+b²)² - (ab)²

= (a²+b²+ab) (a²+b²-ab)

= (a²+ab+b²) (a²-ab+b²)

(This cannot be further factorised. That's why, this will be considered as the final result.)

Used formula :

• (x+y)² = x²+2xy+y²
• x²-y² = (x+y) (x-y)

Hence, the answer to the factorisation is, (a²+ab+b²) (a²-ab+b²)