Question

factorise
a⁴-2a²b²+b⁴

Answer 1

Answer:((a-b)(a+b))2

Step-by-step explanation:

By using formula;

(a2-b2)2

((a-b)(a+b))2

Answer 2

Given,

a⁴-2a²b²+b⁴

To find,

The factors of a⁴-2a²b²+b⁴.

Solution,

The factors of a⁴-2a²b²+b⁴ will be (a²-b²)².

We can easily solve this problem by following the given steps.

According to the question,

a⁴-2a²b²+b⁴

Now, we can find its factors using the identity method because the other two methods of factorising by splitting the middle term or by taking out common do not work.

The expression can be re-written as follows:

(a²)²+(b²)²-2(a²)(b²)

Now, it fits in the identity of (a-b)² = a²+b²-2ab.

In this case, a = a² and b = b².

So, it will be

(a²-b²)²

Hence, the factors of a⁴-2a²b²+b⁴ are (a²-b²)².