Question

factorise a^4-2a^2b^2+b^4

Answer 1

a4-2a2b2+b4
= (a2-b2)2
= (a+b)2(a-b)2

Answer 2

Answer:

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

Explanation:

Given algebraic expression:

a⁴-2a²b²+b⁴

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we know the algebraic identity:

x²-2xy+y² = (x-y)²

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Factorisation of a⁴-2a²b²+b⁴

= (a²)²-2*a²*b²+(b²)²

= (a²-b²)²

=(a²-b²)(a²-b²)

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We know the algebraic identity:

x²-y² = (x+y)(x-y)

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= (a-b)(a+b)(a-b)(a+b)

Therefore,

a⁴-2a²b²+b⁴

= (a-b)(a+b)(a-b)(a+b)

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